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One of the most promising strategies to test gravity in the strong-field, large curvature regime is gravitational spectroscopy: the measurement of black hole quasi-normal modes from the ringdown signal emitted in the aftermath of a compact binary coalescence, searching for deviations from the predictions of general relativity. This strategy is only effective if we know how quasi-normal modes of black holes are affected by modifications of general relativity; and if we know this for rotating black holes, since binary coalescences typically lead to black holes with spins $J/M^2\sim 0.7$. In this article, we compute for the first time the gravitational quasi-normal modes of rotating black holes up to second order in the spin in a modified gravity theory. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest theories which modifies the large-curvature regime of gravity and which can be tested with black hole observations. To enhance the domain of validity of the spin expansion, we perform a Pad\'e resummation of the quasi-normal modes. We find that when the second order in spin is not included, the effect of gravity modifications may be seriously underestimated. A comparison with the general relativistic case suggests that this approach should be accurate up to spins $\sim 0.7$; therefore, our results can be used in the data analysis of ringdown signals., Comment: 19 pages, 6 figures, 5 tables. Minor changes to match the version published in Phys. Rev. D. arXiv admin note: text overlap with arXiv:2103.09870

K. G. Arun et al., 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 gravitational waves 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., E. Berti is supported by NSF Grants No. PHY-1912550 and AST-2006538, NASA ATP Grants No. 17-ATP17-0225 and 19-ATP19-0051, NSF-XSEDE Grant No. PHY-090003, and NSF Grant PHY-20043. D. Blas is supported by a ‘Ayuda Beatriz Galindo Senior’ from the Spanish ‘Ministerio de Universidades’, grant BG20/00228. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. The research leading of to these results has received funding from the Spanish Ministry of Science and Innovation (PID2020-115845GB-I00/AEI/10.13039/501100011033). K. Clough is supported by funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 693024). A. Cárdenas-Avendaño acknowledges funding from the Fundación Universitaria Konrad Lorenz (Project 5INV1) and from Will and Kacie Snellings. M. Crisostomi and E. Barausse are supported by the European Union’s H2020 ERC Consolidator Grant “GRavity from Astrophysical to Microscopic Scales” (Grant No. GRAMS-815673). P. Fleury received the support of a fellowship from “la Caixa” Foundation (ID 100010434). The fellowship code is LCF/BQ/PI19/11690018. C. Herdeiro thanks the support of the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020, the projects PTDC/FIS-OUT/28407/2017, CERN/FIS-PAR/0027/2019, PTDC/FIS-AST/3041/2020 and the European Union’s Horizon 2020 research and innovation (RISE) programme H2020-MSCA-RISE-2017 Grant No. FunFiCO-777740. P. Pani and E. Maggio acknowledge financial support provided under the European Union’s H2020 ERC, Starting Grant agreement no. DarkGRA–757480, and under the MIUR PRIN and FARE programmes (GW-NEXT, CUP: B84I20000100001), and support from the Amaldi Research Center funded by the MIUR program “Dipartimento di Eccellenza” (CUP: B81I18001170001). N.Frusciante was supported by Fundação para a Ciência e a Tecnologia (FCT) through the research grants UIDB/04434/2020, UIDP/04434/2020, PTDC/FIS-OUT/29048/2017, CERN/FIS-PAR/0037/2019, the FCT project “CosmoTests—Cosmological tests of gravity theories beyond General Relativity” with ref. number CEECIND/00017/2018 and the FCT project “BEYLA –BEYond LAmbda” with ref. number PTDC/FIS-AST/0054/2021. L.Lombriser was supported by a Swiss National Science Foundation Professorship grant (No. 170547). S.N. acknowledges support from the Alexander von Humboldt Foundation. D.N. acknowledges support from the NSF Grant No. PHY-2011784. R.B. acknowledges financial support from FCT – Fundação para a Ciência e a Tecnologia, I.P., under the Scientific Employment Stimulus - Individual Call - 2020.00470.CEECIND. V. Paschalidis acknowledges support from NSF Grant PHY-1912619 and NASA Grant 80NSSC20K1542 to the University of Arizona. B.S.S. is supported by NSF grants No. AST-2006384 and PHY-2012083. C.F.S. is supported by contracts ESP2017-90084-P and PID2019-106515GB-I00/AEI/10.13039/501100011033 (Spanish Ministry of Science and Innovation) and 2017-SGR-1469 (AGAUR, Generalitat de Catalunya). T. P. S. acknowledges partial support from the STFC Consolidated Grant No. ST/P000703/1. M. Ruiz acknowledges support from NASA Grant 80NSSC17K0070 to the University of Illinois at Urbana-Champaign. I.D. Saltas is supported by the Czech Science Foundation GAČR, Grant No. 21-16583M. N. Stergioulas is supported by the ESA Prodex grant PEA:4000132310 “LISA Stochastic Signals Analysis Pipeline”. F.V. acknowledges partial support from CNES. K.Y. acknowledges support from NSF Grant PHY-1806776, NASA Grant 80NSSC20K0523, a Sloan Foundation Research Fellowship and the Owens Family Foundation. K.Y. would like to also acknowledge support by the COST Action GWverse CA16104 and JSPS KAKENHI Grants No. JP17H06358. N. Yunes acknowledges support from NASA Grants No. NNX16AB98G, 80NSSC17M0041 and 80NSSC18K1352, NSF Award No. 1759615, and the Simons Foundation through MPS Award Number 896696. D.D. acknowledge financial support via an Emmy Noether Research Group funded by the German Research Foundation (DFG) under grant no. DO 1771/1-1.

The gravitational wave signal from a binary neutron star merger carries the imprint of the deformability properties of the coalescing bodies, and then of the equation of state of neutron stars. In current models of the waveforms emitted in these events, the contribution of tidal deformation is encoded in a set of parameters, the tidal Love numbers. More refined models include tidal-rotation couplings, described by an additional set of parameters, the rotational tidal Love numbers, which appear in the waveform at $6.5$ post-Newtonian order. For neutron stars with spins as large as $\sim0.1$, we show that neglecting tidal-rotation couplings may lead to a significant error in the parameter estimation by third-generation gravitational wave detectors. By performing a Fisher matrix analysis we assess the measurability of rotational tidal Love numbers, showing that their contribution in the waveform could be measured by third-generation detectors. Our results suggest that current models of tidal deformation in late inspiral should be improved in order to avoid waveform systematics and extract reliable information from gravitational wave signals observed by next generation detectors., 11 pages, 4 figures

We study binary systems in which a stellar mass compact object spirals into a massive black hole, known as extreme mass ratio inspirals, in scenarios with a new fundamental scalar field. Earlier work has shown that, in most interesting such scenarios and to leading order in the mass ratio, the massive black holes can be adequately approximated by the Kerr metric and the imprint of the scalar field on the waveform is fully controlled by the scalar charge of the stellar mass object. Here we use this drastic simplification in the inspiral modelling and consider eccentric equatorial orbits. We study how the scalar charge affects the orbital evolution for different eccentricities and different values of the black hole spin. We then determine how changes in the orbital evolution get imprinted on the waveform and assess LISA's capability to detect or constrain the scalar charge., Minor changes to match the version published on Phys. Rev. D

The Laser Interferometer Space Antenna, LISA, will detect gravitational wave signals from Extreme Mass Ratio Inspirals, where a stellar mass compact object orbits a supermassive black hole and eventually plunges into it. Here we report on LISA's capability to detect whether the smaller compact object in an Extreme Mass Ratio Inspiral is endowed with a scalar field, and to measure its scalar charge -- a dimensionless quantity that acts as a measure of how much scalar field the object carries. By direct comparison of signals, we show that LISA will be able to detect and measure the scalar charge with an accuracy of the order of percent, which is an unprecedented level of precision. This result is independent of the origin of the scalar field and of the structure and other properties of the small compact object, so it can be seen as a generic assessment of LISA's capabilities to detect new fundamental fields., Typo corrected to match the version in press

The ability to model the evolution of compact binaries from the inspiral to coalescence is central to gravitational wave astronomy. Current waveform catalogues are built from vacuum binary black hole models, by evolving Einstein equations numerically and complementing them with knowledge from slow-motion expansions. Much less is known about the coalescence process in the presence of matter, or in theories other than General Relativity. Here, we explore the Close Limit Approximation as a powerful tool to understand the coalescence process in general setups. In particular, we study the head-on collision of two equal-mass, compact but horizonless objects. Our results show the appearance of ``echoes'' and indicate that a significant fraction of the merger energy goes into these late-time repetitions. We also apply the Close Limit Approximation to investigate the effect of colliding black holes on surrounding scalar fields. Notably, our results indicate that observables obtained through perturbation theory may be extended to a significant segment of the merger phase, where in principle only a numerical approach is appropriate., 16 pages, 4 figures. Matches published version in CQG

Gravitational spectroscopy - the measurement of the quasi-normal modes of a black hole from the ringdown signal of a binary black hole coalescence - is one of the most promising tools to test gravity in the strong-field, large-curvature regime, but without the knowledge of the black hole quasi-normal modes in specific cases of modified gravity theories, only null tests of general relativity are possible. More specifically, we need to know the modes of rotating black holes, because typical compact binary mergers lead to black holes with large spins. In this article we compute, for the first time, the gravitational quasi-normal modes of rotating black holes in a modified gravity theory, up to first order in the spin. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest modifications of general relativity in the large-curvature regime. We find that the shifts in the mode frequencies and damping times due to general relativity modifications are significantly magnified by rotation., Comment: 13 pages, 3 figures, 1 table. Typos corrected and references added

The coupling between the angular momentum of a compact object and an external tidal field gives rise to the "rotational" tidal Love numbers, which affect the tidal deformability of a spinning self-gravitating body and enter the gravitational waveform of a binary inspiral at high post-Newtonian order. We provide numerical evidence for a surprising "hidden" symmetry among the rotational tidal Love numbers with opposite parities, which are associated to perturbations belonging to separate sectors. This symmetry, whose existence had been suggested on the basis of a Lagrangian description of the tidal interaction in a binary system, holds independently of the equation of state of the star., Comment: 13 pages, 2 figures; minor changes

We study Extreme Mass Ratio Inspirals (EMRIs), during which a small body spirals into a supermassive black hole, in gravity theories with additional scalar fields. We first argue that no-hair theorems and the properties of known theories that manage to circumvent them introduce a drastic simplification to the problem: the effects of the scalar on supermassive black holes, if any, are mostly negligible for EMRIs in vast classes of theories. We then exploit this simplification to model the inspiral perturbatively and we demonstrate that the scalar charge of the small body leaves a significant imprint on gravitational wave emission. Although much higher precision is needed for waveform modelling, our results strongly suggest that this imprint is observable with LISA, rendering EMRIs promising probes of scalar fields., Minor changes to match the version in press on Phys. Rev. Lett

Scalar Gauss-Bonnet gravity is the only theory with quadratic curvature corrections to general relativity whose field equations are of second differential order. This theory allows for nonperturbative dynamical corrections and is therefore one of the most compelling case studies for beyond-general relativity effects in the strong-curvature regime. However, having second-order field equations is not a guarantee for a healthy time evolution in generic configurations. As a first step towards evolving black-hole binaries in this theory, we here derive the 3+1 decomposition of the field equations for any (not necessarily small) coupling constant and we discuss potential challenges of its implementation., 8 pages

Containing the latest, groundbreaking discoveries in the field, this text outlines the basics of Einstein’s theory of gravity with a focus on its most important astrophysical consequences, including stellar structures, black holes and the physics of gravitational waves. Blending advanced topics - usually not found in introductory textbooks - with examples, pedagogical boxes, mathematical tools and practical applications of the theory, this textbook maximises learning opportunities and is ideal for master and graduate students in Physics and Astronomy. Key features:• Provides a self-contained and consistent treatment of the subject that does not require advanced previous knowledge of the field.• Explores the subject with a new focus on gravitational waves and astrophysical relativity, unlike current introductory textbooks.• Fully up-to-date, containing the latest developments and discoveries in the field.

Gravitational-wave (GW) observations provide a wealth of information on the nature and properties of black holes. Among these, tidal Love numbers or the multipole moments of the inspiralling and final objects are key to a number of constraints. Here, we consider these observations in the context of higher-dimensional scenarios, with flat large extra dimensions. We show that -- as might be anticipated, but not always appreciated in the literature -- physically motivated set-ups are unconstrained by gravitational-wave data. Dynamical processes that do not excite the Kaluza-Klein (KK) modes lead to a signal identical to that in four-dimensional general relativity in vacuum . In addition, any possible excitation of the KK modes is highly suppressed relative to the dominant quadrupolar term; given existing constraints on the extra dimensions and the masses of the objects seen in gravitational-wave observations, KK modes appear at post-Newtonian order $\sim 10^{11}$. Finally, we re-compute the tidal Love numbers of spherical black holes in higher dimensions. We confirm that these are different from zero, but comparing with previous computations we find a different magnitude and sign., 8 pages, RevTeX 4. v2: Minor corrections, version to appear in Physical Review D

Black-hole spectroscopy is arguably the most promising tool to test gravity in extreme regimes and to probe the ultimate nature of black holes with unparalleled precision. These tests are currently limited by the lack of a ringdown parametrization that is both robust and accurate. We develop an observable-based parametrization of the ringdown of spinning black holes beyond general relativity, which we dub ParSpec (Parametrized Ringdown Spin Expansion Coefficients). This approach is perturbative in the spin, but it can be made arbitrarily precise (at least in principle) through a high-order expansion. It requires O(10) ringdown detections, which should be routinely available with the planned space mission LISA and with third-generation ground-based detectors. We provide a preliminary analysis of the projected bounds on parametrized ringdown parameters with LISA and with the Einstein Telescope, and discuss extensions of our model that can be straightforwardly included in the future., Comment: 15 pages, 8 figures. v2: matches published version

It has recently been shown that nontrivial couplings between a scalar and the Gauss-Bonnet invariant can give rise to black hole spontaneous scalarization. Theories that exhibit this phenomenon are among the leading candidates for testing gravity with upcoming black hole observations. All models considered so far have focused on specific forms for the coupling, neglecting scalar self-interactions. In this work, we take the first steps towards placing this phenomenon on a more robust theoretical footing by considering the leading-order scalar self-interactions as well as the scalar-Gauss-Bonnet coupling. Our approach is consistent with the principles of effective field theory and yields the simplest and most natural model. We find that a mass term for the scalar alters the threshold for the onset of scalarization, and we study the mass range over which scalarized black hole solutions exist. We also demonstrate that the quartic self-coupling is sufficient to produce scalarized solutions that are stable against radial perturbations, without the need to resort to higher-order terms in the Gauss-Bonnet coupling function. Our model therefore represents a canonical model that can be studied further, with the ultimate aim of developing falsifiable tests of black hole scalarization., 10 Pages, six figures

We study the nonlinear dynamics of black holes that carry scalar hair and binaries composed of such black holes. The scalar hair is due to a linear or exponential coupling between the scalar and the Gauss--Bonnet invariant. We work perturbatively in the coupling constant of that interaction but nonperturbatively in the fields. We first consider the dynamical formation of hair for isolated black holes of arbitrary spin and determine the final state. This also allows us to compute for the first time the scalar quasinormal modes of rotating black holes in the presence of this coupling. We then study the evolution of nonspinning black-hole binaries with various mass ratios and produce the first scalar waveform for a coalescence. An estimate of the energy loss in scalar radiation and the effect this has on orbital dynamics and the phase of the GWs (entering at quadratic order in the coupling) show that GW detections can set the most stringent constraint to date on theories that exhibit a coupling between a scalar field and the Gauss--Bonnet invariant., Comment: 24 pages; 12 figures; Numerical code based on the Einstein Toolkit with new thorns available at https://bitbucket.org/canuda/. v2: updated references and discussion

We develop a new method to measure neutron star parameters and derive constraints on the equation of state of dense matter by fitting the frequencies of simultaneous Quasi Periodic Oscillation modes observed in the X-ray flux of accreting neutron stars in low mass X-ray binaries. To this aim we calculate the fundamental frequencies of geodesic motion around rotating neutron stars based on an accurate general-relativistic approximation for their external spacetime. Once the fundamental frequencies are related to the observed frequencies through a QPO model, they can be fit to the data to obtain estimates of the three parameters describing the spacetime, namely the neutron star mass, angular momentum and quadrupole moment. From these parameters we derive information on the neutron star structure and equation of state. We present a proof of principle of our method applied to pairs of kHz QPO frequencies observed from three systems (4U1608-52, 4U0614+09 and 4U1728-34). We identify the kHz QPOs with the azimuthal and the periastron precession frequencies of matter orbiting the neutron star, and via our Bayesian inference technique we derive constraints on the neutrons stars' masses and radii. This method is applicable to other geodesic-frequency-based QPO models., Comment: Changes to match the version in press on ApJ

We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss-Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well., Comment: v2: Five pages, three figures. Minor corrections, references added. v3: Matches version published in Phys. Rev. Lett

In this brief note, we clarify certain aspects related to the magnetic (i.e., odd parity or axial) tidal Love numbers of a star in general relativity. Magnetic tidal deformations of a compact star had been computed in 2009 independently by Damour and Nagar and by Binnington and Poisson. More recently, Landry and Poisson showed that the magnetic tidal Love numbers depend on the assumptions made on the fluid, in particular they are different (and of opposite sign) if the fluid is assumed to be in static equilibrium or if it is irrotational. We show that the zero-frequency limit of the Regge-Wheeler equation forces the fluid to be irrotational. For this reason, the results of Damour and Nagar are equivalent to those of Landry and Poisson for an irrotational fluid, and are expected to be the most appropriate to describe realistic configurations., Comment: v2: 4 pages, one extra equation. Matches the PRD version

With the doors beginning to swing open on the new gravitational wave astronomy, this review provides an up-to-date survey of the most important physical mechanisms that could lead to emission of potentially detectable gravitational radiation from isolated and accreting neutron stars. In particular we discuss the gravitational wave-driven instability and asteroseismology formalism of the f- and r-modes, the different ways that a neutron star could form and sustain a non-axisymmetric quadrupolar “mountain” deformation, the excitation of oscillations during magnetar flares and the possible gravitational wave signature of pulsar glitches. We focus on progress made in the recent years in each topic, make a fresh assessment of the gravitational wave detectability of each mechanism and, finally, highlight key problems and desiderata for future work.

Light bosonic fields are ubiquitous in extensions of the Standard Model. Even when minimally coupled to gravity, these fields might evade the assumptions of the black-hole no-hair theorems and give rise to spinning black holes which can be drastically different from the Kerr metric. Furthermore, they allow for self-gravitating compact solitons, known as (scalar or Proca) boson stars. The quasiperiodic oscillations (QPOs) observed in the x-ray flux emitted by accreting compact objects carry information about the strong-field region, thus providing a powerful tool to constrain deviations from Kerr’s geometry and to search for exotic compact objects. By using the relativistic precession model as a proxy to interpret the QPOs in terms of geodesic frequencies, we investigate how the QPO frequencies could be used to test the no-hair theorem and the existence of light bosonic fields near accreting compact objects. We show that a detection of two QPO triplets with current sensitivity can already constrain these models and that the future eXTP mission or a LOFT-like mission can set very stringent constraints on black holes with bosonic hair and on (scalar or Proca) boson stars. The peculiar geodesic structure of compact scalar/Proca boson stars implies that these objects can easily be ruled out as alternative models for x-ray source GRO J1655-40.

Several quantum-gravity models of compact objects predict microscopic or even Planckian corrections at the horizon scale. We explore the possibility of measuring two model-independent, smoking-gun effects of these corrections in the gravitational waveform of a compact binary, namely the absence of tidal heating and the presence of tidal deformability. For events detectable by the future space-based interferometer LISA, we show that the effect of tidal heating dominates and allows one to constrain putative corrections down to the Planck scale. The measurement of the tidal Love numbers with LISA is more challenging but, in optimistic scenarios, it allows to constrain the compactness of a supermassive exotic compact object down to the Planck scale. Our analysis suggests that highly-spinning, supermassive binaries at 1-20 Gpc provide unparalleled tests of quantum-gravity effects at the horizon scale., Comment: v4: matches version in Phys. Rev. Lett; Editors' Suggestion

Generalizations of the Schwarzschild and Kerr black holes are discussed in an astrophysically viable generalized theory of gravity, which includes higher curvature corrections in the form of the Gauss-Bonnet term, coupled to a dilaton. The angular momentum of these black holes can slightly exceed the Kerr bound. The location and the orbital frequency of particles in their innermost stable circular orbits can deviate significantly from the respective Kerr values. Study of the quasinormal modes of the static black holes gives strong evidence that they are mode stable against polar and axial perturbations. Future gravitational wave observations should improve the current bound on the Gauss-Bonnet coupling constant, based on observations of the low-mass x-ray binary A 0620-00., Comment: 8 pages, 7 figures

In a core-collapse supernova, a huge amount of energy is released in the Kelvin-Helmholtz phase subsequent to the explosion, when the proto-neutron star cools and deleptonizes as it loses neutrinos. Most of this energy is emitted through neutrinos, but a fraction of it can be released through gravitational waves. We model the evolution of a proto-neutron star in the Kelvin-Helmholtz phase using a general relativistic numerical code, and a recently proposed finite temperature, many-body equation of state; from this we consistently compute the diffusion coefficients driving the evolution. To include the many-body equation of state, we develop a new fitting formula for the high density baryon free energy at finite temperature and intermediate proton fraction. We estimate the emitted neutrino signal, assessing its detectability by present terrestrial detectors, and we determine the frequencies and damping times of the quasi-normal modes which would characterize the gravitational wave signal emitted in this stage., Comment: 25 pages, 14 figures, accepted by PRD

Supermassive binaries detectable by the future space gravitational-wave interferometer LISA might allow to distinguish black holes from ultracompact horizonless objects, even when the latter are motivated by quantum-gravity considerations. We show that a measurement of very small tidal Love numbers at the level of $10\%$ accuracy (as achievable with "golden binaries") may also allow to distinguish between different models of these exotic compact objects, even when taking into account an intrinsic uncertainty in the object radius putatively due to quantum mechanics. We argue that there is no conceptual obstacle in performing these measurements, the main challenge remains the detectability of small tidal effects and an accurate waveform modelling. Our analysis uses only coordinate-independent quantities related to the proper radial distance and the total mass of the object., Comment: Minor changes to match the version published on CQG

We review recent progress in the application of numerical relativity techniques to astrophysics and high-energy physics. We focus on some developments that took place within the "Numerical Relativity and High Energy Physics" network, a Marie Curie IRSES action that we coordinated, namely: spin evolution in black hole binaries, high-energy black hole collisions, compact object solutions in scalar-tensor gravity, superradiant instabilities and hairy black hole solutions in Einstein's gravity coupled to fundamental fields, and the possibility to gain insight into these phenomena using analog gravity models., 46 pages, 6 figures; Submitted to a Special Issue of IJMPD on Selected Papers of the III Amazonian Symposium on Physics