Search

Precise measurements of neutron star observables (such as mass and radius) allow one to constrain the equations of state for supranuclear matter and develop a stronger understanding of nuclear physics. The Neutron star Interior Composition ExploreR (NICER) tracks X-ray hotspots on rotating NSs and is able to infer precise information about the compactness of the star. Gravitational waves carry information about the tidal deformability (related to the tidal Love number) of neutron stars, which has been measured by the LIGO/Virgo/KAGRA collaboration. These two observables enjoy an approximately universal property between each other that is insensitive to the equations of state (the "universal Love-C relation"). In this paper, we focus on deriving two analytic expressions for the Love-C relations that are ready-to-use and improve upon previous analytic expressions. The first model is inspired by a Newtonian polytrope, whose perturbation to the gravitational potential can be found analytically. We extend this Newtonian model to the relativistic regime by providing a quadratic fit to the gravitational potential perturbation against stellar compactness. The second model makes use of the Tolman VII model and adopts a spectral expansion with Chebyshev polynomials, which converges faster than the Taylor expansions used in previous work. We find that the first model provides a more accurate description of the Love-C relation for realistic neutron stars than the second model, and it provides the best expression among all other analytic relations studied here in terms of describing the averaged numerical Love-C relation. These new models are not only useful in practice, but they also show the power and importance of analytic modeling of neutron stars., Comment: 11 pages, 9 figures

Tidal effects on compact objects provide profound theoretical insights into the structure of the field equations, and are wonderful probes of the equation of state of matter, the nature of black holes and of the underlying theory of gravity. The natural framework for understanding tides is a perturbative scheme. Here, we point out ambiguities in determining tidal response functions within such a framework, which may lead to bias in constraining physical parameters with gravitational-wave observations if the computed quantities are not properly linked to observables. We propose a Canonical Tidal Response Function (CTRF) definition to compare values of tides in theories beyond vacuum General Relativity in a unified manner. As an example, we provide black hole tidal response functions, including both conservative and dissipative pieces, in various theories of gravity. Tidal dissipation Love numbers for black holes are derived here for the first time in most of the non-Einsteinian theories considered in this paper., Comment: 24 pages

The response of astrophysical compact objects to external tidal fields carries valuable information on the nature of these objects, on the equation of state of matter, and on the underlying gravitational theory. In this work, we highlight subtleties in describing relativistic dynamical tidal responses that arise from ambiguities in the decomposition of a perturbed metric into external tidal and induced response pieces. Observables are unambiguous. However in practice, differences arising from implicit assumptions in the definition of tidal deformabilities may lead to a bias in constraining nuclear physics or gravitational theories, if not properly tied to observational data. We propose calibration of a tidal response function for any compact objects in vacuum General Relativity. Within this framework, the dynamical tidal Love numbers of a Schwarzschild black hole in both even and odd sectors vanish at any multipole order. The calibration allows one to define dynamical tidal deformabilities of relativistic stars, such as neutron stars, as the difference from the BH values (zero) under the unified definition in a simple manner. As a straightforward extension of our framework, we compute the next-to-leading dissipative tidal response of Schwarzschild black holes for the first time., Comment: 22 pages

Gravitational waves have been shown to provide new constraints on gravitational theories beyond general relativity (GR), especially in the strong field regime. Gravitational wave signals from galactic double white dwarfs, expected to be detected by the Laser Interferometer Space Antenna (LISA), also have the potential to place stringent bounds on certain theories that give rise to relatively large deviations from GR in less compact binaries, such as through scalar radiation. Nevertheless, the orbital evolution of close double white dwarf systems is also affected by various astrophysical effects, such as stellar rotation, tidal interactions, and magnetic interactions, which add complexity to the gravity tests. In this work, we employ the parametrized post-Einsteinian model to capture the leading beyond-GR effect on the signal and estimate the measurement uncertainties using the Fisher information matrix. We then study the systematic error caused by ignoring each astrophysical effect mentioned above on the parameter estimation. Our numerical results show that, to place bounds on the non-GR effects comparable to existing bounds from pulsar observations, tight priors on the mass of the binary and long observation time are required. At this level of sensitivity, we found that systematic errors from the astrophysical effects dominate statistical errors. The most significant effects investigated here are torques from tidal synchronization and magnetic unipolar induction for sufficiently large magnetic fields ($>10^7$G). Meanwhile, even the weaker astrophysical effects from quadrupolar deformations are of a similar order of magnitude as the statistical uncertainty, and hence cannot be ignored in the waveform model. We conclude that the astrophysical effects must be carefully accounted for in the parameter estimation to test gravity with galactic double white dwarfs detected by LISA., Comment: 14 pages, 8 figures, submitted to PRD

A massive black hole can develop a dark-matter overdensity, and the dark matter changes the evolution of a stellar-mass compact object inspiraling around the massive black hole through the dense dark-matter environment. Specifically, dynamical friction speeds up the inspiral of the compact object and causes feedback on the dark-matter distribution. These intermediate mass-ratio inspirals with dark matter are a source of gravitational waves (GWs), and the waves can dephase significantly from an equivalent system in vacuum. Prior work has shown that this dephasing needs to be modeled to detect the GWs from these systems with LISA (the Laser Interferometer Space Antenna); it also showed that the density and distribution of dark matter can be inferred from a GW measurement. In this paper, we study whether the parametrized post-Einsteinian (ppE) framework can be used to infer the presence of dark matter in these systems. We confirm that if vacuum waveform templates are used to model the GWs from an inspiral in a dark-matter halo, then the resulting parameter estimation is biased. We then apply the ppE framework to determine whether it can reduce the parameter-estimation biases, and we find that adding one ppE phase term to a waveform template eliminates the parameter-estimation biases (statistical errors become larger than the systematic ones), but the effective post-Newtonian order in the ppE framework must be specified without uncertainties. When the post-Newtonian order has uncertainty, we find that the systematic errors on the ppE and the binary's parameters exceed the statistical errors. Thus, the simplest ppE framework would not give unbiased results for these systems, and a further extension of it, or dedicated parameter estimation with gravitational waveforms that include dark-matter effects would be needed., Comment: 16 pages, 8 figures

Quasiperiodic oscillations (QPOs) have been recently discovered in the short gamma-ray bursts (GRBs) 910711 and 931101B. Their frequencies are consistent with those of the radial and quadrupolar oscillations of binary neutron star merger remnants, as obtained in numerical relativity simulations. These simulations reveal quasiuniversal relations between the remnant oscillation frequencies and the tidal coupling constant of the binaries. Under the assumption that the observed QPOs are due to these postmerger oscillations, we use the frequency-tide relations in a Bayesian framework to infer the source redshift, as well as the chirp mass and the binary tidal deformability of the binary neutron star progenitors for GRBs 910711 and 931101B. We further use this inference to estimate bounds on the mass-radius relation for neutron stars. By combining the estimates from the two GRBs, we find a 68\% credible range $R_{1.4}=12.48^{+0.41}_{-0.41}$~km for the radius of a neutron star with mass $M=1.4$~M$_\odot$, which is one of the tightest bounds to date.

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves are allowing us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical \emph{extreme gravity regime}. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review then discusses gravitational-wave tests using compact binary systems, and ends with a description of the first gravitational wave observations by advanced LIGO, the stochastic gravitational wave background observations by pulsar timing arrays, and the tests that can be performed with them.., Comment: Update to Living Rev.Rel. 16 (2013) 9, now with twice the content and three times the number of references! arXiv admin note: substantial text overlap with arXiv:1304.3473

Neutron stars (NSs) provide a unique laboratory to study matter under extreme densities. Recent observations from gravitational and electromagnetic waves have enabled constraints on NS properties, such as tidal deformability (related to the tidal Love number) and stellar compactness. Although each of these two NS observables depends strongly on the stellar internal structure, the relation between them (called the Love-C relation) is known to be equation-of-state insensitive. In this study, we investigate the effects of a possible crystalline phase in the core of hybrid stars (HSs) on the mass-radius and Love-C relations, where HSs are a subclass of NS models with a quark matter core and a nuclear matter envelope with a sharp phase transition in between. We find that both the maximum mass and the corresponding radius increase as one increases the stiffness of the quark matter core controlled by the speed of sound, while the density discontinuity at the nuclear-quark matter transition effectively softens the equations of state. Deviations of the Love-C relation for elastic HSs from that of fluid NSs become more pronounced with a larger shear modulus, lower transition pressure, and larger density gap and can be as large as 60%. These findings suggest a potential method for testing the existence of distinct phases within HSs, though deviations are not large enough to be detected with current measurements of the tidal deformability and compactness., Comment: 29 pages, 12 figures, Accepted for publication in General Relativity and Gravitation

Non-radial oscillation modes of a neutron star possess valuable information about its internal structure and nuclear physics. Starting from the quadrupolar order, such modes under general relativity are known as quasi-normal modes since they dissipate energy through gravitational radiation and their frequencies are complex. The stability of these modes is governed by the sign of the imaginary part of the frequency, which determines whether the mode would decay or grow over time. In this Letter, we develop a fully consistent framework in general relativity to study quasi-normal modes of neutron stars with anisotropic pressure, whose motivation includes strong internal magnetic fields and non-vanishing shear or viscosity. We employ parametrized models for the anisotropy and solve the perturbed Einstein field equations numerically. We find that, unlike the case for isotropic neutron stars, the imaginary parts of some of the pressure ($p$-)modes flip signs as the degree of anisotropy deviates from zero, depicting a transition from stable modes to unstable modes. This finding indicates that some anisotropic neutron star models are unstable, potentially restricting the form of sustained anisotropy., Comment: 8+6 pages, 2+1 figures, re-submitted to PRD

General relativity (GR) has proven to be a highly successful theory of gravity since its inception. The theory has thrivingly passed numerous experimental tests, predominantly in weak gravity, low relative speeds, and linear regimes, but also in the strong-field and very low-speed regimes with binary pulsars. Observable gravitational waves (GWs) originate from regions of spacetime where gravity is extremely strong, making them a unique tool for testing GR, in previously inaccessible regions of large curvature, relativistic speeds, and strong gravity. Since their first detection, GWs have been extensively used to test GR, but no deviations have been found so far. Given GR's tremendous success in explaining current astronomical observations and laboratory experiments, accepting any deviation from it requires a very high level of statistical confidence and consistency of the deviation across GW sources. In this paper, we compile a comprehensive list of potential causes that can lead to a false identification of a GR violation in standard tests of GR on data from current and future ground-based GW detectors. These causes include detector noise, signal overlaps, gaps in the data, detector calibration, source model inaccuracy, missing physics in the source and in the underlying environment model, source misidentification, and mismodeling of the astrophysical population. We also provide a rough estimate of when each of these causes will become important for tests of GR for different detector sensitivities. We argue that each of these causes should be thoroughly investigated, quantified, and ruled out before claiming a GR violation in GW observations., Comment: Review article; 1 figure; 1 table; comments welcome

The response of black holes to small perturbations is known to be partially described by a superposition of quasinormal modes. Despite their importance to enable strong-field tests of gravity, little to nothing is known about what overtones and quasinormal-mode amplitudes are like for black holes in extensions to general relativity. We take a first step in this direction and study what is arguably the simplest model that allows first-principle calculations to be made: a nonrotating black hole in an effective-field-theory extension of general relativity with cubic-in-curvature terms. Using a phase-amplitude scheme that uses analytical continuation and the Pr\"ufer transformation, we compute, for the first time, the quasinormal overtone frequencies (in this theory) and quasinormal-mode excitation factors (in any theory beyond general relativity). We find that the overtone quasinormal frequencies and their excitation factors are more sensitive than the fundamental mode to the lengthscale $l$ introduced by the higher-derivative terms in the effective field theory. We argue that a description of all overtones cannot be made within the regime of validity of the effective field theory, and we conjecture that this is a general feature of any extension to general relativity that introduces a new lengthscale. We also find that a parametrization of the modifications to the general-relativistic quasinormal frequencies in terms of the ratio between $l$ and the black hole's mass is somewhat inadequate, and we propose a better alternative. As an application, we perform a preliminary study of the implications of the breakdown, in the effective field theory, of the equivalence between the quasinormal mode spectra associated to metric perturbations of polar and axial parity of the Schwarzschild black hole in general relativity. We also present a simple justification for the loss of isospectrality., Comment: 21 pages, 9 figures, 1 table. (v2) Matches version published in Phys. Rev. D

Certain relations among neutron-star observables that are insensitive to the equation of state are known to exist. Such universal relations have been shown to be valid for cold and stationary neutron stars. Here, we study these relations in more dynamic scenarios: protoneutron stars and hypermassive neutron stars. First, we study protoneutron stars. We use an effective equation of state, extracted from three-dimensional core-collapse supernova simulations, to obtain the structure of spherically symmetric protoneutron stars. We then consider nonradial oscillations to compute their $f$-mode frequency ($f$), as well as slow rotation and small tidal deformation, to compute their moment of inertia ($I$), spin-induced quadrupole moment ($Q$), and Love number. We find that well-established universal relations for cold neutron stars involving these observables ($I$-Love-$Q$ and $f$-Love relations) are approximately valid for protoneutron stars, with a deviation below $\approx$ 10$\%$ for a postbounce time above $\approx$ 0.5 s, considering eight different supernova progenitors and the SFHo equation of state. Next, we study hypermassive neutron stars. We obtain a new universal relation between the $f$-mode frequency and the compactness of cold and nonrotating neutron stars, using bulk quantities. We show that this relation has an equation-of-state-variation of $\approx$ $3\%$, considering a set of ten equations of state. Using results from binary neutron star merger simulations, we study the evolution of hypermassive neutron stars on the $f$-$C$ plane, considering two different mass ratios and the SFHo equation of state. We find that the relation between the peak frequency of the gravitational-wave signal and the compactness from these hypermassive neutron stars deviates from the universal $f$-$C$ relation by 70 $-$ 80$\%$, when the peak frequency is taken directly as a proxy for the $f$-mode.

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

Parameterized Kerr spacetimes allow us to test the nature of black holes in model-independent ways. Such spacetimes contain several arbitrary functions and, as a matter of practicality, one Taylor expands them about infinity and keeps only to finite orders in the expansion. In this paper, we focus on the parameterized spacetime preserving Killing symmetries of a Kerr spacetime and show that an unphysical divergence may appear in the metric if such a truncation is performed in the series expansion. To remedy this, we redefine the arbitrary functions so that the divergence disappears, at least for several known black hole solutions that can be mapped to the parameterized Kerr spacetime. We propose two restricted classes of the refined parameterized Kerr spacetime that only contain one or two arbitrary functions and yet can reproduce exactly all the example black hole spacetimes considered in this paper. The Petrov class of the parameterized Kerr spacetime is of type I while that for the restricted class with one arbitrary function remains type D. We also compute the ringdown frequencies and the shapes of black hole shadows for the parameterized spacetime and show how they deviate from Kerr. The refined black hole metrics with Kerr symmetries presented here are practically more useful than those proposed in previous literature., Comment: 21 pages, 8 figures; added an appendix and references; accepted for publication in PRD

Accreting binary white dwarf systems are among the sources expected to emanate gravitational waves that the Laser Interferometer Space Antenna (LISA) will detect. We investigate how accurately the binary parameters may be measured from LISA observations. We complement previous studies by performing our parameter estimation on binaries containing a low-mass donor with a thick, hydrogen-rich envelope. The evolution is followed from the early, pre-period minimum stage, in which the donor is non-degenerate, to a later, post-period minimum stage with a largely degenerate donor. We present expressions for the gravitational wave amplitude, frequency, and frequency derivative in terms of white dwarf parameters (masses, donor radius, etc.), where binary evolution is driven by gravitational wave radiation and accretion torques, and the donor radius and logarithmic change in radius ($\eta_{\rm d}$) due to mass loss are treated as model parameters. We then perform a Fisher analysis to reveal the accuracy of parameter measurements, using models from Modules for Experiments in Stellar Astrophysics (MESA) to estimate realistic fiducial values at which we evaluate the measurement errors. We find that the donor radius can be measured relatively well with LISA observations alone, while we can further measure the individual masses if we have an independent measurement of the luminosity distance from electromagnetic observations. When applied to the parameters of the recently-discovered white dwarf binary ZTF J0127+5258, our Fisher analysis suggests that we will be able to constrain the system's individual masses and donor radius using LISA's observations, given ZTF's measurement of the luminosity distance.

We revisit the classic problem of gravitational wave emission by a test particle plunging into a Schwarzschild black hole both in the frequency-domain Regge-Wheeler-Zerilli formalism and in the semirelativistic approximation. We use, and generalize, a transformation due to Nakamura, Sasaki, and Shibata to improve the falloff of the source term of the Zerilli function. The faster decay improves the numerical convergence of quantities of interest, such as the energy radiated at spatial infinity through gravitational waves. As a test of the method, we study the gravitational radiation produced by test particles that plunge into the black hole with impact parameters close to the threshold for scattering. We recover and expand upon previous results that were obtained using the Sasaki-Nakamura equation. In particular, we study the relative contributions to the total energy radiated due to waves of axial and polar parity, and uncover an universal behavior in the waveforms at late times. We complement our study with a semirelativistic analysis of the problem, and we compare the two approaches. The generalized Nakamura-Sasaki-Shibata transformation presented here is a simple and practical alternative for the analysis of gravitational-wave emission by unbound orbits in the Schwarzschild spacetime using the frequency-domain Regge-Wheeler-Zerilli formalism., Comment: 16 pages, 10 figures. v2. Matches published version

In some modified theories of gravity, gravitational waves can contain up to six different polarizations, which can travel at speeds different from that of light. Searches for these different polarizations in gravitational wave data are important because any detection would be clear evidence of new physics, while clear non-detections could constrain some modified theories. The first step toward searching the data for such gravitational wave content is the calculation of the amplitudes of these different polarizations. Here we present a model-independent method to obtain the different polarizations of gravitational waves directly from the metric perturbation in theories where these polarizations are allowed to travel at different speeds. We develop our calculations so that the same procedure works with either the metric perturbation itself or its trace-reversed form. Our results are in agreement with previous work in the limit that all polarization speeds are the speed of light. We demonstrate how our model-independent method can be used with two specific modified theories of gravity, suggesting its wide applicability to other theories that allow for different gravitational wave propagation speeds. We further extend the parametrized post-Einsteinian formalism to apply to such theories that travel with different speeds. Finally, we discuss how the different speeds of different polarizations may affect null stream tests of general relativity with gravitational wave observations by multiple interferometers. Differences in propagation speeds may make null streams ineffective or lead to the detection of what seem to be isolated scalar or vector modes., Comment: 13 pages; replaced with accepted version

Although Lorentz symmetry is a staple of General Relativity (GR), there are several reasons to believe it may not hold in a more advanced theory of gravity, such as quantum gravity. Einstein-aether theory is a modified theory of gravity that breaks Lorentz symmetry by introducing a dynamical vector field called the aether. The theory has four coupling constants that characterize deviations from GR and that must be determined through observations. Although three of the four parameters have been constrained by various empirical observations and stability requirements, one, called $c_\omega$, remains essentially unconstrained. The aim of this work is to see if a constraint on $c_\omega$ can be derived from the I-Love-Q universal relations for neutron stars, which connect the neutron star moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q) in a way that is insensitive to uncertainties in the neutron star equation-of-state. To understand if the theory can be constrained through such relations, we model slowly-rotating or weakly tidally-deformed neutron stars in Einstein-aether theory, derive their I-Love-Q relations, and study how they depend on $c_\omega$. We find that the I-Love-Q relations in Einstein-aether theory are insensitive to $c_\omega$ and that they are close to the relations in GR. This means that the I-Love-Q relations in Einstein-aether theory remain universal but cannot be used to constrain the theory. These results indicate that to constrain the theory with neutron stars, it is necessary to investigate relations involving other observables., Comment: 20 pages, 6 figures

Lorentz symmetry is a fundamental property of Einstein's theory of general relativity that one may wish to test with gravitational wave observations. Einstein-aether theory is a model that introduces Lorentz-symmetry breaking in the gravitational sector through an aether vector field, while still leading to second-order field equations. This well-posed theory passes particle physics constraints because it modifies directly only the gravitational sector, yet it predicts deviations in the inspiral and coalescence of compact objects. We here, for the first time, put this theory to the test by comparing its gravitational wave predictions directly against LIGO/Virgo gravitational wave data. We construct a waveform model for Einstein-aether theory, EA_IMRPhenomD_NRT, through modifications of the general relativity IMRPhenomD_NRTidalv2 model (used by the LIGO/VIRGO collaboration). This model constructs a reponse function that not only contains the transverse-traceless polarization, but also additional Einstein-aether (scalar and vectorial) polarizations simultaneously. We then use the many current constraints on the theory to construct non-trivial priors for the Einstein-aether coupling constants. After testing the waveform model, we conduct parameter estimation studies on two gravitational wave events: GW170817 and GW190425. We find that these data are not sufficiently informative to place constraints on the theory that are stronger than current bounds from binary pulsar, solar system and cosmological observations. This is because, although Einstein-aether modifications include additional polarizations and have been computed beyond leading post-Newtonian order, these modifications are dominated by (already-constrained) dipole effects. These difficulties make it unclear whether future gravitational wave observations will be able to improve on current constraints on Einstein-aether theory., Comment: 32 pages, 24 figures

Allowing for the possibility of extra dimensions, there are two paradigms: either the extra dimensions are hidden from observations by being compact and small as in Kaluza-Klein scenarios, or the extra dimensions are large/non-compact and undetectable due to a large warping as in the Randall-Sundrum scenario. In the latter case, the five-dimensional background has a large curvature, and Isaacson's construction of the gravitational energy-momentum tensor, which relies on the assumption that the wavelength of the metric fluctuations is much smaller than the curvature length of the background spacetime, cannot be used. In this paper, we construct the gravitational energy-momentum tensor in a strongly curved background such as Randall-Sundrum. We perform a scalar-vector-tensor decomposition of the metric fluctuations with respect to the $SO(1,3)$ background isometry and construct the covariantly-conserved gravitational energy-momentum tensor out of the gauge-invariant metric fluctuations. We give a formula for the power radiated by gravitational waves and verify it in known cases. In using the gauge-invariant metric fluctuations to construct the gravitational energy-momentum tensor we follow previous work done in cosmology. Our framework has applicability beyond the Randall-Sundrum model., Comment: 54 pages, minor typos fixed, section 4.A expanded, conclusions added

The distance-inclination degeneracy limits gravitational-wave parameter estimation of compact binary mergers. Although the degeneracy can be partially broken by including higher-order modes or precession, these effects are suppressed in binary neutron stars. In this work, we implement a new parametrization of the tidal effects in the binary neutron-star waveform, exploiting the binary Love relations, that breaks the distance-inclination degeneracy. The binary Love relations prescribe the tidal deformability of a neutron star as a function of its source-frame mass in an equation-of-state insensitive way and, thus, allows direct measurement of the redshift of the source. If the cosmological parameters are assumed to be known, the redshift can be converted to a luminosity distance, and the distance-inclination degeneracy can thus be broken. We implement this new approach, studying a range of binary neutron-star observing scenarios using Bayesian parameter estimation on synthetic data. In the era of the third-generation detectors, for observations with signal-to-noise ratios ranging from 6 to 167, we forecast up to an $\sim70\%$ decrease in the $90\%$ credible interval of the distance and inclination and up to an $\sim50\%$ decrease in that of the source-frame component masses. For edge-on systems, our approach can result in moderate ($\sim50\%$) improvement in the measurements of distance and inclination for binaries with a signal-to-noise ratio as low as 10. This prescription can be used to better infer the source-frame masses and, hence, refine population properties of neutron stars, such as their maximum mass, impacting nuclear astrophysics. When combined with the search for electromagnetic counterpart observations, the work presented here can be used to put improved bounds on the opening angle of jets from binary neutron-star mergers., Comment: 19 pages, 13 figures, text and references updated, v2 matches version published in PRD

The dynamical tide can play an important role in the orbital motion of close eccentric double white dwarf binaries. As the launching of the space-based gravitational-wave detector, the Laser Interferometer Space Antenna (LISA), is just around the corner, detection of gravitational wave signals from such systems is anticipated. In this paper, we discuss the influence of the dynamical tide on eccentric orbits, focusing on the effect on orbital precession. We show that in orbits with a high eccentricity, resonance can cause a large precession when a harmonic of the orbital frequency matches the natural frequencies of the normal modes of the star. In contrast to the case with circular orbits, each mode can encounter multiple resonances with different harmonics and these resonant regions can cover about 10% of the frequency space for orbits with close separations. In this case, the tidal precession effect is distinct from the other contributions and can be identified with LISA if the signal-to-noise ratio is high enough. However, within the highly eccentric-small separation region, the dynamical tide causes chaotic motion and the gravitational wave signal becomes unpredictable. Even not at resonance, the dynamical tide can contribute up to 20% of the precession for orbits close to Roche-lobe filling separation with low eccentricities and LISA can resolve these off-resonant dynamical tide effects within the low eccentricity-small orbital separation region of the parameter space. For lower mass systems, the dynamical tide effect can degenerate with the uncertainties of the eccentricity, making it unmeasurable from the precession rate alone. For higher mass systems, the radiation reaction effect becomes significant enough to constrain the eccentricity, allowing the measurement of the dynamical tide., Comment: 13 pages. 9 figures

Neutron stars are versatile in their application to studying various important aspects of fundamental physics, in particular strong-field gravity tests and the equation of state for super-dense nuclear matter at low temperatures. However, in many cases these two objectives are degenerate to each other. We discuss how pulsar timing and gravitational waves provide accurate measurements of neutron star systems and how to effectively break the degeneracy using tools like universal relations. We also present perspectives on future opportunities and challenges in the field of neutron star physics., Comment: 5 pages, 2 figures; accepted by Science Bulletin

Recent observations indicate that magnetars may commonly reside in merging compact binaries and at least part of fast radio bursts (FRBs) are sourced by magnetar activities. It is natural to speculate that a class of merging neutron star binaries may have FRB emitters. In this work, we study the observational aspects of these binaries - particularly those with FRB repeaters, which are promising multi-band and multi-messenger observation targets of radio telescopes and ground based gravitational wave detectors as the former telescopes can probe the systems at a much earlier stage in the inspiral than the latter. We show that observations of FRB repeaters in compact binaries have a significant advantage in pinning down the binary spin dynamics, constraining neutron star equation of state, probing FRB production mechanisms, and testing beyond standard physics. As a proof of principle, we investigate several mock observations of FRB pulses originating from pre-merger neutron star binaries, and we find that using the information of FRB arriving times alone, the intrinsic parameters of this system (including the stellar masses, spins, and quadrupole moments) can be measured with high precision, and the angular dependence of the FRB emission pattern can also be well reconstructed. The measurement of stellar masses (with an error of $\mathcal{O}(10^{-6}-10^{-5})$) and quadrupole moments (with an error of $\mathcal{O}(1\%-10\%)$) may be an unprecedented discriminator of nuclear equations of state in neutron stars. In addition, we find the multi-band and multi-messenger observations of this binary will be sensitive to alternative theories of gravity and beyond standard models, e.g., dynamical Chern-Simons gravity and axion field that is coupled to matter., Comment: 20 pages, 12 figs

Ho\v{r}ava-Lifshitz gravity is an alternative theory to general relativity which breaks Lorentz invariance in order to achieve an ultraviolet complete and power-counting renormalizable theory of gravity. In the low energy limit, Ho\v{r}ava-Lifshitz gravity coincides with a vector-tensor theory known as khronometric gravity. The deviation of khronometric gravity from general relativity can be parametrized by three coupling constants: $\alpha$, $\beta$, and $\lambda$. Solar system experiments and gravitational wave observations impose stringent bounds on $\alpha$ and $\beta$, while $\lambda$ is still relatively unconstrained ($\lambda\lesssim 0.01$). In this paper, we study whether one can constrain this remaining parameter with neutron star observations through the universal I-Love-Q relations between the moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q), which are insensitive to details in the nuclear matter equation of state. To do so, we perturbatively construct slowly-rotating and weakly tidally-deformed neutron stars in khronometric gravity. We find that the I-Love-Q relations are independent of $\lambda$ in the limit $(\alpha,\beta) \to 0$. Although some components of the field equations depend on $\lambda$, we show through induction and a post-Minkowskian analysis that slowly-rotating neutron stars do not depend on $\lambda$ at all. Tidally deformed neutron stars, on the other hand, are modified in khronometric gravity (though the usual Love number is not modified, as mentioned earlier), and there are potentially new, non-GR Love numbers, though their observability is unclear. These findings indicate that it may be difficult to constrain $\lambda$ with rotating/tidally-deformed neutron stars., Comment: 18 pages. Added a new Appendix, added additional explanation to Sects. II and III, and added a small clarification to Sect. V, no change to main results

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., Comment: Accepted in: Living Reviews in Relativity

Neutron stars are a remarkable marriage of Einstein's theory of general relativity with nuclear physics. Their interiors harbor extreme matter that cannot be probed in the laboratory. At such high densities and pressures, their cores may consist predominantly of exotic matter such as free quarks or hyperons. Gravitational wave observations from the Laser Interferometer Gravitational-wave Observatory (LIGO) and from other interferometers, and X-ray observations from the Neutron Star Interior Composition Explorer (NICER), are beginning to pierce through the veil. These observations provide information about neutron star cores, and therefore, about the physics that makes such objects possible. In this review, we discuss what we have learned about the physics of neutron stars from gravitational wave and X-ray observations. We focus on what has been observed with certainty and what should be observable in the near future, with an eye out for the physics that these new observations will teach us., Comment: Published in Nature Reviews Physics (2022)

In this chapter, we review the eikonal technique to analytically derive approximate quasi-normal mode frequencies of black holes. We first review the procedure in General Relativity and extend it to theories beyond General Relativity. As an example of the latter, we focus on scalar Gauss-Bonnet gravity in which a scalar field can couple to the Gauss-Bonnet invariant in an arbitrary way in the action. In this theory, metric and scalar perturbations are coupled in the polar sector, forcing the isospectrality to break and making the eikonal calculation more complex. We show that the analytic estimates can accurately capture the numerical behavior of the quasi-normal mode frequencies, especially when the coupling constant of the theory is small., Comment: 17 pages, 5 figures; to appear in a book by China Science Publishing and Media, based on lectures at 2021 Summer School on Early Universe and Gravitational Wave Physics

Recent gravitational wave observations allow us to probe gravity in the strong and dynamical field regime. In this paper, we focus on testing Einstein-dilaton Gauss-Bonnet gravity which is motivated by string theory. In particular, we use two new neutron star black hole binaries (GW200105 and GW200115). We also consider GW190814 which is consistent with both a binary black hole and a neutron star black hole binary. Adopting the leading post-Newtonian correction and carrying out a Bayesian Markov-chain Monte Carlo analyses, we derive the 90\% credible upper bound on the coupling constant of the theory as $\sqrt{\alpha_{GB}} \lesssim 1.33\,\rm km$, whose consistency is checked with an independent Fisher analysis. This bound is stronger than the bound obtained in previous literature by combining selected binary black hole events in GWTC-1 and GWTC-2 catalogs. We also derive a combined bound of $\sqrt{\alpha_{GB}} \lesssim 1.18\,\rm km$ by stacking GW200105, GW200115, GW190814, and selected binary black hole events. In order to check the validity of the effect of higher post-Newtonian terms, we derive corrections to the waveform phase up to second post Newtonian order by mapping results in scalar-tensor theories to Einstein-dilaton Gauss-Bonnet gravity. We find that such higher-order terms improve the bounds by $14.5\%$ for GW200105 and $6.9\%$ for GW200115 respectively., Comment: 12 pages, 5 figures

The spacetime surrounding compact objects such as neutron stars and black holes provides an excellent place to study gravity in the strong, non-linear, dynamical regime. Here, the effects of strong curvature can leave their imprint on observables which we may use to study gravity. Recently, NICER provided a mass and radius measurement of an isolated neutron star using x-rays, while LIGO/Virgo measured the tidal deformability of neutron stars through gravitational waves. These measurements can be used to test the relation between the tidal deformability and compactness of neutron stars that are known to be universal in general relativity. Here, we take (shift-symmetric) scalar-Gauss-Bonnet gravity (motivated by a low-energy effective theory of a string theory) as an example and study whether one can apply the NICER and LIGO/Virgo measurements to the universal relation to test the theory. To do so, this paper is mostly devoted on theoretically constructing tidally-deformed neutron star solutions in this theory perturbatively and calculate the tidal deformability for the first time. We find that the relation between the tidal deformability and compactness remains to be mostly universal for a fixed dimensionless coupling constant of the theory though the relation is different from the one in general relativity. We also present a universal relation between the tidal deformability \textbf{of} one neutron star and the compactness for another neutron star that can be directly applied to observations by LIGO/Virgo and NICER. For the equations of state considered in this paper, it is still inconclusive whether one can place a meaningful bounds on scalar Gauss-Bonnet gravity with the new universal relations. However, we found a new bound from the mass measurement of the pulsar J0740+6620 that is comparable to other existing bounds from black hole observations., Comment: 21 pages, 10 figures, updated to version accepted for publication in Phys. Rev. D

The science objectives of the LISA mission have been defined under the implicit assumption of a 4 yr continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of $\approx 0.75$, which would reduce the effective span of usable data to 3 yr. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 yr of mission operations is recommended., Comment: 50 pages, 19 figures, 5 tables. Matches version published in GERG

Gravitational-wave (GW) memory effects produce permanent shifts in the GW strain and its time integrals after the passage of a burst of GWs. Their presence is closely tied to symmetries of asymptotically flat spacetimes and fluxes of conserved charges conjugate to these symmetries. While the phenomenology of GW memory effects is well understood in general relativity (GR), it is less well understood in the many modifications to GR. We recently computed asymptotically flat solutions, symmetries, conserved quantities, and GW memory effects in one such modified theory: Brans-Dicke theory. In this paper, we apply our results from this earlier work to compute the GW memories from compact binaries in the post-Newtonian (PN) approximation. In addition to taking the PN limit of these effects, we work in the approximation that the energy and angular momentum losses through scalar radiation are small compared to the energy and angular momentum losses through (tensor) GWs. We focus on the tensor (as opposed to scalar) GW memory effect, which we compute through Newtonian order, and the small differences induced by scalar radiation at this order. Specifically, we compute the nonlinear parts of the tensor displacement and spin GW memory effects produced during the inspiral of quasicircular, nonprecessing binaries in Brans-Dicke theory. Because the energy radiated through the scalar dipole moment appears as a -1 PN order-effect, then in this approximation, the displacement memory has a logarithmic dependence on the PN parameter and the spin memory has a relative -1 PN-order correction; these corrections are ultimately small because they are related to the total energy and angular momentum radiated in the scalar field, respectively. At Newtonian order, the scalar radiation also gives rise to a sky pattern of the memory effect around an isolated source that differs from that of the memory effect in GR., Comment: 24 pages; v2: matches published version

In a recent series of papers we have shown how the eikonal/geometrical optics approximation can be used to calculate analytically the fundamental quasinormal mode frequencies associated with coupled systems of wave equations, which arise, for instance, in the study of perturbations of black holes in gravity theories beyond General Relativity. As a continuation to this series, we here focus on the quasinormal modes of nonrotating black holes in scalar Gauss-Bonnet gravity assuming a small-coupling expansion. We show that the axial perturbations are purely tensorial and are described by a modified Regge-Wheeler equation, while the polar perturbations are of mixed scalar-tensor character and are described by a system of two coupled wave equations. When applied to these equations, the eikonal machinery leads to axial modes that deviate from the general relativistic results at quadratic order in the Gauss-Bonnet coupling constant. We show that this result is in agreement with an analysis of unstable circular null orbits around blackholes in this theory, allowing us to establish the geometrical optics-null geodesic correspondence for the axial modes. For the polar modes the small-coupling approximation forces us to consider the ordering between eikonal and small-coupling perturbative parameters; one of which we show, by explicit comparison against numerical data, yields the correct identification of the quasinormal modes of the scalar-tensor coupled system of wave equations. These corrections lift the general relativistic degeneracy between scalar and tensorial eikonal quasinormal modes at quadratic order in Gauss-Bonnet coupling in a way reminiscent of the Zeeman effect. In general, our analytic, eikonal quasinormal mode frequencies (normalized to the General Relativity ones) agree with numerical results with an error of $\sim 10\%$ in the regime of small coupling constant. (abridged), Comment: 15 pages, 4 figures; accepted to PRD

Gravitational-wave cosmology began in 2017 with the observation of the gravitational waves emitted in the merger of two neutron stars, and the coincident observation of the electromagnetic emission that followed. Although only a $30\%$ measurement of the Hubble constant was achieved, future observations may yield more precise measurements either through other coincident events or through cross correlation of gravitational-wave events with galaxy catalogs. Here, we implement a new way to measure the Hubble constant without an electromagnetic counterpart and through the use of the binary Love relations. These relations govern the tidal deformabilities of neutron stars in an equation-of-state insensitive way. Importantly, the Love relations depend on the component masses of the binary in the source frame. Since the gravitational-wave phase and amplitude depend on the chirp mass in the observer (and hence redshifted) frame, one can in principle combine the binary Love relations with the gravitational-wave data to directly measure the redshift, and thereby infer the value of the Hubble constant. We implement this approach in both real and synthetic data through a Bayesian parameter estimation study in a range of observing scenarios. We find that for the LIGO/Virgo/KAGRA design sensitivity era, this method results in a similar measurement accuracy of the Hubble constant to those of current-day, dark-siren measurements. For third generation detectors, this accuracy improves to $\lesssim 10\%$ when combining measurements from binary neutron star events in the LIGO Voyager era, and to $\lesssim 2\%$ in the Cosmic Explorer era., Comment: accepted in PRD

Neutron stars are ideal astrophysical sources to probe general relativity due to their large compactnesses and strong gravitational fields. For example, binary pulsar and gravitational wave observations have placed stringent bounds on certain scalar-tensor theories in which a massless scalar field is coupled to the metric through matter. A remarkable phenomenon of neutron stars in such scalar-tensor theories is spontaneous scalarization, where a normalized scalar charge remains order unity even if the matter-scalar coupling vanishes asymptotically far from the neutron star. While most works on scalarization of neutron stars focus on numerical analysis, this paper aims to derive accurate scalar charges analytically. To achieve this, we consider a simple energy density profile of the Tolman VII form and work in a weak-field expansion. We solve the modified Tolman-Oppenheimer-Volkoff equations order by order and apply Pad\'e resummation to account for higher-order effects. We find that our analytic scalar charges in terms of the stellar compactness beautifully model those computed numerically. We also find a quasi-universal relation between the scalar charge and stellar binding energy that is insensitive to the underlying equations of state. Comparison of analytic scalar charges for Tolman VII and constant density stars mathematically support this quasi-universal relation. The analytic results found here provide physically motivated, ready-to-use accurate expressions for scalar charges., Comment: 13 pages, 9 figures; accepted for publication in Phys. Rev. D

The timing of millisecond pulsars has long been used as an exquisitely precise tool for testing the building blocks of general relativity, including the strong equivalence principle and Lorentz symmetry. Observations of binary systems involving at least one millisecond pulsar have been used to place bounds on the parameters of Einstein-{\ae}ther theory, a gravitational theory that violates Lorentz symmetry at low energies via a preferred and dynamical time threading of the spacetime manifold. However, these studies did not cover the region of parameter space that is still viable after the recent bounds on the speed of gravitational waves from GW170817/GRB170817A. The restricted coverage was due to limitations in the methods used to compute the pulsar sensitivities, which parameterize violations of the strong-equivalence principle in these systems. We extend here the calculation of pulsar sensitivities to the parameter space of Einstein-{\ae}ther theory that remains viable after GW170817/GRB170817A. We show that observations of the damping of the period of quasi-circular binary pulsars and of the triple system PSR J0337+1715 further constrain the viable parameter space by about an order of magnitude over previous constraints., Comment: 43 pages, 8 figures; minor changes to match version published in CQG

Gravitational-wave sources can serve as standard sirens to probe cosmology by measuring their luminosity distance and redshift. Such standard sirens are also useful to probe theories beyond general relativity with a modified gravitational-wave propagation. Many of previous studies on the latter assume multi-messenger observations so that the luminosity distance can be measured with gravitational waves while the redshift is obtained by identifying sources' host galaxies from electromagnetic counterparts. Given that gravitational-wave events of binary neutron star coalescences with associated electromagnetic counterpart detections are expected to be rather rare, it is important to examine the possibility of using standard sirens with gravitational-wave observations alone to probe gravity. In this paper, we achieve this by extracting the redshift from the tidal measurement of binary neutron stars that was originally proposed within the context of gravitational-wave cosmology (another approach is to correlate "dark sirens" with galaxy catalogs that we do not consider here). We consider not only observations with ground-based detectors (e.g. Einstein Telescope) but also multi-band observations between ground-based and space-based (e.g. DECIGO) interferometers. We find that such multi-band observations with the tidal information can constrain a parametric non-Einsteinian deviation in the luminosity distance (due to the modified friction in the gravitational wave evolution) more stringently than the case with electromagnetic counterparts by a factor of a few. We also map the above-projected constraints on the parametric deviation to those on specific theories and phenomenological models beyond general relativity to put the former into context., Comment: 14 pages, 12 figures

One of the uncertainties in nuclear physics is whether a phase transition between hadronic nuclear matter to quark matter exists in supranuclear matter equations of state. Such a feature can be probed via gravitational-wave signals from binary neutron star inspirals that contain information of the induced tides. The dynamical part of the tides is caused by the resonance of pulsation modes of stars, which causes a shift in the gravitational-wave phase. In this paper, we investigate the dynamical tides of the interfacial mode ($i$-mode) of spherical degree $l=2$, a non-radial mode caused by an interface associated with a quark-hadron phase transition inside a hybrid star. In particular, we focus on hybrid stars with a crystalline quark matter core and a fluid hadronic envelope. We find that the resonant frequency of such $i$-modes typically ranges from 300Hz to 1500Hz, and the frequency increases as the shear modulus of the quark core increases. We next estimate the detectability of such a mode with existing and future gravitational-wave events from the inspiral waveform with a Fisher analysis. We find that GW170817 and GW190425 have the potential to detect the $i$-mode if the quark-hadron phase transition occurs at sufficiently low pressure and the shear modulus of the quark matter phase is large enough. We also find that the third-generation gravitational-wave detectors can further probe the $i$-mode with intermediate transition pressure. This finding opens a new, interesting direction for probing the existence of quark core inside a neutron star.

Unlike gravitational waves from merging black holes and neutron stars that chirp significantly over the observational period of ground-based detectors, gravitational waves from binary white dwarfs are almost monochromatic. This makes it extremely challenging to measure their individual masses. Here, we take a novel approach of using finite-size effects and applying certain universal relations to measure individual masses of binary white dwarfs using LISA. We found quasi-universal relations among the mass, moment of inertia, and tidal deformability of a white dwarf that do not depend sensitively on the white dwarf composition. These relations allow us to rewrite the moments of inertia and tidal deformabilities in the waveform in terms of the masses. We then carried out a Fisher analysis to estimate how accurately one can measure the individual masses from the chirp mass and finite-size measurements. We found that the individual white dwarf masses can be measured with LISA for a 4-year observation if the initial frequency is high enough ($\sim 0.02$Hz) and either the binary separation is small ($\sim 1$kpc) or the masses are relatively large $(m \gtrsim 0.8M_\odot)$. This opens a new possibility of measuring individual masses of binary white dwarfs with space-based interferometers., Comment: 5 pages, 4 figures; typos in Fig.4 and its caption corrected

Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity with gravitational waves. In particular, we focus on three theory-agnostic tests (parameterized tests, inspiral-merger-ringdown consistency tests, and gravitational-wave propagation tests) and explain how one can apply such tests to example modified theories of gravity. We conclude by giving some open questions that need to be resolved to carry out more accurate tests of gravity with gravitational waves., Comment: v1: Submitted as a chapter in "Handbook of Gravitational Wave Astronomy" (Eds. C. Bambi, S. Katsanevas and K. Kokkotas; Springer Singapore, 2021). The maximum number of allowed references is used; v2, v3: minor corrections to refs

The Neutron star Interior Composition Explorer (NICER) is currently observing the x-ray pulse profiles emitted by hot spots on the surface of rotating neutron stars allowing for an inference of their radii with unprecedented precision. A critical ingredient in the pulse profile model is an analytical formula for the oblate shape of the star. These formulas require a fitting over a large ensemble of neutron star solutions, which cover a wide set of equations of state, stellar compactnesses and rotational frequencies. However, this procedure introduces a source of systematic error, as (i) the fits do not describe perfectly the surface of all stars in the ensemble and (ii) neutron stars are described by a single equation of state, whose influence on the surface shape is averaged out during the fitting procedure. Here we perform a first study of this systematic error, finding evidence that it is subdominant relative to the statistical error in the radius inference by NICER. We also find evidence that the formula currently used by NICER can be used in the inference of the radii of rapidly rotating stars, outside of the formula's domain of validity. Moreover, we employ an accurate enthalpy-based method to locate the surface of numerical solutions of rapidly rotating neutron stars and a new highly accurate formula to describe their surfaces. These results can be used in applications that require an accurate description of oblate surfaces of rapidly rotating neutron stars., Comment: 20 pages, 12 figures, 7 tables, 1 appendix. (v2) Matches version published in Phys. Rev. D

Precision tests of general relativity can be conducted by observing binary pulsars. Theories with massive fields exist to explain a variety of phenomena from dark energy to the strong CP problem. Existing pulsar binaries, such as the white dwarf-pulsar binary J1738+0333, have been used to place stringent bounds on the scalar dipole emission, and radio telescopes may detect a pulsar orbiting a black hole in the future. In this paper, we study the ability of pulsar binaries to probe theories involving massive scalar and vector fields through the measurement of the orbital decay rate. With a generic framework, we describe corrections to orbital decay rate due to (a) modification of GR quadrupolar radiation and (b) dipolar radiation of a massive field. We then consider three concrete examples: (i) massive Brans-Dicke theory, (ii) general relativity with axions, and (iii) general relativity with bound dark matter and a dark force. Finally, we apply direct observations of J1738 and simulations of a black hole-pulsar binary to bound theory parameters such as field's mass and coupling constant. We find new constraints on bound dark matter interactions with PSR J1738, and a black hole-pulsar discovery would likely improve these further. Such bounds are complementary to future gravitational-wave bounds. Regarding other theories, we find similar constraints to previous pulsar measurements for massive Brans-Dicke theory and axions. These results show that new pulsar binaries will continue to allow for more stringent tests of gravity., Comment: minor edits, 12 pages, 3 figures

Gravitational-wave memory effects are identified by their distinctive effects on families of freely falling observers: after a burst of waves pass by their locations, memory effects can cause lasting relative displacements of the observers. These effects are closely related to the infrared properties of gravity and other massless field theories, including their asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in Brans-Dicke theory. We compute the field equations in Bondi coordinates, and we define a set of boundary conditions that represent asymptotically flat solutions in this context. Next, we derive the asymptotic symmetry group of these spacetimes, and we find that it is the same as the Bondi-Metzner-Sachs group in general relativity. Because there is an additional polarization of gravitational waves in Brans-Dicke theory, we compute the memory effects associated with this extra polarization (the so-called "breathing" mode). This breathing mode produces a uniform expansion (or contraction) of a ring of freely falling observers. After these breathing gravitational waves pass by the observers' locations, there are two additional memory effects that depend on their initial displacements and relative velocities. Neither of these additional memory effects seems to be related to asymptotic symmetries or conserved quantities; rather, they are determined by the properties of the nonradiative region before and after the bursts of the scalar field and the gravitational waves. We discuss the properties of these regions necessary to support nontrivial breathing-mode-type memory effects., Comment: Appendix added, section 2B modified, minor modifications to the introduction, matches published version

Noncommutative gravity is a natural method of quantizing spacetime by promoting the spacetime coordinates themselves to operators which do not commute. This approach is motivated, for example, from a quantum gravity perspective, among others. Noncommutative gravity has been tested against the binary black hole merger event GW150914. Here, we extend and improve upon such a previous analysis by (i) relaxing an assumption made on the preferred direction due to noncommutativity, (ii) using posterior samples produced by the LIGO/Virgo Collaborations, (iii) consider other gravitational wave events, namely GW151226, GW170608, GW170814 and GW170817, and (iv) consider binary pulsar observations. Using Kepler's law that contains the noncommutative effect at second post-Newtonian order, we derive corrections to the gravitational waveform phase and the pericenter precession. Using the gravitational wave and double pulsar binary observations, we find bounds on a space-time noncommutative tensor $\theta^{0i}$ in terms of the preferred frame direction with respect to the orientation of each binary. We find that the gravitational wave bounds are stronger than the binary pulsar one by an order of magnitude and the noncommutative tensor normalized by the Planck length and time is constrained to be of order unity., Comment: 9 pages, 5 figures

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy., Comment: 10 pages, 3 figures

Vector-tensor theories beyond General Relativity have widely been studied in the context of ultraviolet completion of gravity, endowing a mass to the graviton and explaining dark energy phenomena. We here construct rotating black hole solutions in vector-tensor theories valid after the binary neutron star merger event GW170817 that placed very stringent bound on the propagation speed of gravitational waves away from the speed of light. Such valid vector-tensor theories are constructed by performing a generic conformal transformation to Einstein-Maxwell theory, and the new rotating black hole solutions are constructed by applying the same conformal transformation to the Kerr-Newman solution. These theories fall outside of beyond generalized Proca theories but are within an extended class of vector-tensor theories that satisfy a degenerate condition to eliminate instability modes and are thus healthy. We find that such conformal Kerr-Newman solutions preserve the location of the singularities, event horizons and ergoregion boundary from Kerr-Newman, as well as the multipole moments and the Petrov type. On the other hand, the Hamilton-Jacobi equation is no longer separable, suggesting that the Carter-like constant does not exist in this solution. The standard Newman-Janis algorithm also does not work to construct the new solutions. We also compute the epicyclic frequencies, the location of the innermost stable circular orbits, and the Schwarzschild precession and apply the latter to the recent GRAVITY measurement to place bounds on the deviations away from Kerr-Newman for Sgr A$^*$., Comment: 12 pages, 3 figures

We study the effect of compact extra dimensions on the gravitational wave luminosity and waveform. We consider a toy model, with a compactified fifth dimension, and matter confined on a brane. We work in the context of five dimensional ($5d$) general relativity, though we do make connections with the corresponding Kaluza-Klein effective $4d$ theory. We show that the luminosity of gravitational waves emitted in $5d$ gravity by a binary with the same characteristics (same masses and separation distance) as a $4d$ binary is 20.8\% less relative to the $4d$ case, to leading post-Newtonian order. The phase of the gravitational waveform differs by 26\% relative to the $4d$ case, to leading post-Newtonian order. Such a correction arises mainly due to the coupling between matter and dilaton field in the effective $4d$ picture and agrees with previous calculations when we set black holes' scalar charges to be those computed from the Kaluza-Klein reduction. The above corrections to the waveform and the luminosity are inconsistent with the gravitational-wave and binary pulsar observations and thus they effectively rule out the possibility of such a simple compactified higher dimensions scenario. We also comment on how our results change if there are several compactified extra dimensions, and show that the discrepancy with $4d$ general relativity only increases., Comment: 33 pages, 1 figure, updated references, expanded discussion

Recent observations of gravitational waves from binary black holes and neutron stars allow us to probe the strong and dynamical field regime of gravity. On the other hand, a collective signal from many individual, unresolved sources results in what is known as a stochastic background. We here consider probing gravity with such a background from stellar-mass binary black hole mergers. We adopt a simple power-law spectrum and carry out a parameter estimation study with a network of current and future ground-based detectors by including both general relativistic and beyond general relativistic variables. For a network of second-generation detectors, we find that one can place meaningful bounds on the deviation parameter in the gravitational-wave amplitude if it enters at a sufficiently negative post-Newtonian order. However, such future bounds from a stochastic background are weaker than existing bounds from individual sources, such as GW150914 and GW151226. We also find that systematic errors due to mismodeling of the spectrum is much smaller than statistical errors, which justifies our use of the power-law model. Regarding a network of third-generation detectors, we find that the bounds on the deviation parameter from statistical errors improve upon the second-generation case, though systematic errors now dominate the error budget and thus one needs to use a more realistic spectrum model. We conclude that individual sources seem to be more powerful in probing general relativity than the astrophysical stochastic background., Comment: 10 pages, 6 figures, submitted to Phys. Rev. D

Recent observations of neutron stars (NS) with radio, X-rays and gravitational waves have begun to constrain the equation of state (EoS) for nuclear matter beyond the nuclear saturation density. To one's surprise, there exist approximate universal relations connecting certain bulk properties of NSs that are insensitive to the underlying EoS and having important applications on probing fundamental physics including nuclear and gravitational physics. To date, analytic works on universal relations for realistic NSs are lacking, which may lead to a better understanding of the origin of the universality. Here, we focus on the universal relations between the compactness(C), moment of inertia (I), and tidal deformability(related to the Love number), and derive analytic, approximate I-Love-C relations. To achieve this, we construct slowly-rotating/ tidally-deformed NS solutions analytically starting from an extended Tolman VII model that accurately describes non-rotating realistic NSs, allowing us to extract the moment of inertia and the tidal deformability on top of the compactness. We solve the field equations analytically by expanding them about the Newtonian limit and keeping up to 6th order in the stellar compactness. Based on these analytic solutions, we can mathematically demonstrate the O(10%) EoS variation in the I-C and Love-C relations and the O(1%) variation in the I-Love relation that have previously been found numerically. Our new analytic relations agree more accurately with numerical results for realistic NSs(especially the I-C and Love-C ones) than the analytic relations for constant density stars derived in previous work. Based on these analytic findings, we attribute a possible origin of the universality for the I-C and Love-C relations to the fact that the energy density of realistic NSs can be approximated as a quadratic function, as is the case for the Tolman VII solution., Comment: Corrections on Fig.1 and Fig.2, in which the correct curve corresponding to constant density case(Love-C panel) replaced the wrong one

Gravitational waves from the explosive merger of distant black holes are encoded with details regarding the complex extreme-gravity spacetime present at their source. Famously described by the Kerr spacetime metric for rotating black holes in general relativity, what if effects beyond this theory are present? One way to efficiently test this hypothesis is to first obtain a metric which parametrically deviates from the Kerr metric in a model-independent way. Given such a metric, one can then predict the ensuing corrections to both the inspiral and ringdown portions of the gravitational waveform for black holes present in the new spacetime. With these tools in hand, one can then test gravitational wave signals for such effects by two different methods, (i) inspiral-merger-ringdown consistency test, and (ii) parameterized test. In this paper, we demonstrate the exact recipe one needs to do just this. We first derive parameterized corrections to the waveform inspiral, ringdown, and remnant properties for a generic non-Kerr spacetime and apply this to two example beyond-Kerr spacetimes each parameterized by a single non-Kerr parameter. We then predict the beyond-Kerr parameter magnitudes required in an observed gravitational wave signal to be statistically inconsistent with the Kerr case in general relativity. We find that the two methods give very similar bounds. The constraints found with existing gravitational-wave events are comparable to those from x-ray observations, while future gravitational-wave observations using Cosmic Explorer (Laser Interferometer Space Antenna) can improve such bounds by two (three) orders of magnitude., Comment: 18 pages, 4 figures; Updated to match published version