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Gravitational waveform (GW) models are a core ingredient for the analysis of compact binary mergers observed by current ground-based interferometers. We focus here on a specific class of such models known as PhenomX, which has gained popularity in recent years thanks to its computational efficiency. We introduce a new description of the ``twisting-up'' mapping underpinning the construction of precessing waveforms within this family. The new description is an adaptation to the frequency domain of a technique previously implemented in time-domain models, where the orbit-averaged post-Newtonian spin-precession dynamics is numerically solved on the fly. We also present an improved version of the gravitational-wave strain amplitudes approximating the signal in the co-precessing frame. We demonstrate that the new description yields improved matches against numerical relativity simulations, with only a modest computational overhead. We also show that the new model can be reliably employed in parameter estimation follow-ups of GW events, returning equivalent or more stringent measurements of the source properties compared to its predecessor., Comment: 17 pages, 10 figures

General Relativity (GR) remains the most accurate theory of gravity to date. It has passed many experimental tests in the Solar System as well as binary pulsar, cosmological and gravitational-wave (GW) observations. Some of these tests probe regimes where gravitational fields are weak, the spacetime curvature is small, and the characteristic velocities are not comparable to the speed of light. Observations of compact binary coalescences enable us to test GR in extreme environments of strong and dynamical gravitational fields, large spacetime curvature, and velocities comparable to the speed of light. Since the breakthrough observation of the first GW signal produced by the merger of two black holes, GW150914, in September 2015, the number of confirmed detections of binary mergers has rapidly increased to nearly 100. The analysis of these events has already placed significant constraints on possible deviations from GR and on the nature of the coalescing compact objects. In this chapter, we discuss a selection of tests of GR applicable to observations of GWs from compact binaries. In particular, we will cover consistency tests, which check for consistency between the different phases of the binary's evolution, tests of GW generation, polarization and propagation, and tests of the remnant's nature. We conclude with a brief overview of the challenges and prospects for present and future observatories., Comment: 36 pages, 8 figures, Review Chapter for the book "Recent Progress on Gravity Tests" (Eds. C. Bambi and A. C\'ardenas-Avenda\~no, Springer Singapore)

We investigate the prospect of performing a null test of binary black hole (BBH) nature using spin-induced quadrupole moment (SIQM) measurements. This is achieved by constraining a deviation parameter ($\delta\kappa$) related to the parameter ($\kappa$) that quantifies the degree of deformation due to the spin of individual binary components on leading (quadrupolar) spin-induced moment. Throughout the paper, we refer to $\kappa$ as the SIQM parameter and $\delta\kappa$ as the SIQM-deviation parameter. The test presented here extends the earlier SIQM-based null tests for BBH nature by employing waveform models that account for double spin-precession and higher modes. We find that waveform with double spin-precession gives better constraints for $\delta\kappa$, compared to waveform with single spin-precession. We also revisit earlier constraints on the SIQM-deviation parameter for selected GW events observed through the first three observing runs (O1-O3) of LIGO-Virgo detectors. Additionally, the effects of higher-order modes on the test are also explored for a variety of mass-ratio and spin combinations by injecting simulated signals in zero-noise. Our analyses indicate that binaries with mass-ratio greater than 3 and significant spin precession may require waveforms that account for spin-precession and higher modes to perform the parameter estimation reliably., Comment: 13 pages, 7 figures

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

The general-relativistic phenomenon of spin-induced orbital precession has not yet been observed in strong-field gravity. Gravitational-wave observations of binary black holes (BBHs) are prime candidates, since we expect the astrophysical binary population to contain precessing binaries. Imprints of precession have been investigated in several signals, but no definitive identification of orbital precession has been reported in any one of the 84 BBH observations to date by the Advanced LIGO and Virgo detectors. Here we report the measurement of strong-field precession in the LIGO-Virgo-Kagra (LVK) gravitational-wave signal GW200129. The binary's orbit precesses at a rate ten orders of magnitude faster than previous weak-field measurements from binary pulsars. We also find that the primary black hole is likely highly spinning. According to current binary population estimates a GW200129-like signal is extremely unlikely, and therefore presents a direct challenge to many current binary formation models., Comment: 16 pages, 6 figures. Update to match published version

In this paper we present an extensive analysis of the GW190521 gravitational wave event with the current (fourth) generation of phenomenological waveform models for binary black hole coalescences. GW190521 stands out from other events since only a few wave cycles are observable. This leads to a number of challenges, one being that such short signals are prone to not resolve approximate waveform degeneracies, which may result in multi-modal posterior distributions. The family of waveform models we use includes a new fast time-domain model IMRPhenomTPHM, which allows us extensive tests of different priors and robustness with respect to variations in the waveform model, including the content of spherical harmonic modes. We clarify some issues raised in a recent paper [Nitz&Capano], associated with possible support for a high-mass ratio source, but confirm their finding of a multi-modal posterior distribution, albeit with important differences in the statistical significance of the peaks. In particular, we find that the support for both masses being outside the PISN mass-gap, and the support for an intermediate mass ratio binary are drastically reduced with respect to what Nitz&Capano found. We also provide updated probabilities for associating GW190521 to the potential electromagnetic counterpart from ZTF., Comment: 20 pages, 13 figures, 7 tables. Data release at https://zenodo.org/record/4751655

We present IMRPhenomTPHM, a phenomenological model for the gravitational wave signals emitted by the coalescence of quasi-circular precessing binary black holes systems. The model is based on the "twisting up" approximation, which maps non-precessing signals to precessing ones in terms of a time dependent rotation described by three Euler angles, and which has been utilized in several frequency domain waveform models that have become standard tools in gravitational wave data analysis. Our model is however constructed in the time domain, which allows several improvements over the frequency domain models: we do not use the stationary phase approximation, we employ a simple approximation for the precessing Euler angles for the ringdown signal, and we implement a new method for computing the Euler angles through the evolution of the spin dynamics of the system, which is more accurate and also computationally efficient., Comment: 18 pages, 10 figures, 4 tables

We consider the ten confidently detected gravitational-wave signals in the GWTC-1 catalog which are consistent with mergers of binary black hole systems, and perform a thorough parameter estimation re-analysis. This is made possible by using computationally efficient waveform models of the current (fourth) generation of the IMRPhenom family of phenomenological waveform models, which consists of the IMRPhenomX frequency-domain modelsand the IMRPhenomT time-domain models. The analysis is performed with both precessing and non-precessing waveform models with and without subdominant spherical harmonic modes. Results for all events are validated with convergence tests, discussing in particular the events GW170729 and GW151226. For the latter and the other two lowest-mass events, we also compare results between two independent sampling codes, Bilby and LALInference. We find overall consistent results with the original GWTC-1 results, with all Jensen-Shannon divergences between the previous results using IMRPhenomPv2 and our default IMRPhenomXPHM posteriors below 0.045 bits, but we also discuss cases where including subdominant harmonics and/or precession influences the posteriors., Comment: 24 pages, 19 figures, 9 tables matches version accepted by MNRAS

In this work we present an extension of the time domain phenomenological model IMRPhenomT for gravitational wave signals from binary black hole coalescences to include subdominant harmonics, specifically the $(l=2, m=\pm 1)$, $(l=3, m=\pm 3)$, $(l=4, m=\pm 4)$ and $(l=5, m=\pm 5)$ spherical harmonics. We also improve our model for the dominant $(l=2, m=\pm 2)$ mode and discuss mode mixing for the $(l=3, m=\pm 2)$ mode. The model is calibrated to numerical relativity solutions of the full Einstein equations up to mass ratio 18, and to numerical solutions of the Teukolsky equations for higher mass ratios. This work complements the latest generation of traditional frequency domain phenomenological models (IMRPhenomX), and provides new avenues to develop computationally efficient models for gravitational wave signals from generic compact binaries., Comment: 22 pages, 18 figures. https://dcc.ligo.org/P2000524

We re-analyse the gravitational-wave event GW190412 with state-of-the-art phenomenological waveform models. This event, which has been associated with a black hole merger, is interesting due to the significant contribution from subdominant harmonics. We use both frequency-domain and time-domain waveform models. The PhenomX waveform models constitute the fourth generation of frequency-domain phenomenological waveforms for black hole binary coalescence; they have more recently been complemented by the time-domain PhenomT models, which open up new strategies to model precession and eccentricity, and to perform tests of general relativity with the phenomenological waveforms approach. Both PhenomX and PhenomT have been constructed with similar techniques and accuracy goals, and due to their computational efficiency this "generation X" model family allows the routine use of subdominant spherical harmonics in Bayesian inference. We show the good agreement between these and other state-of-the-art waveform models for GW190412, and discuss the improvements over the previous generation of phenomenological waveform models. We also discuss practical aspects of Bayesian inference such as run convergence, variations of sampling parameters, and computational cost., Comment: 25 pages, 18 figures. Data release: https://doi.org/10.5281/zenodo.4079188

In this work we present IMRPhenomTP, a time domain phenomenological model for the dominant $l=2$, $m=|2|$ modes of coalescing black hole binary systems and its extension to describe general precessing systems within the "twisting up" approximation. The underlying non-precessing model is calibrated to the new release of Numerical Relativity simulations of the SXS Collaboration and its accuracy is comparable to the state-of-the-art non-precessing dominant mode models as IMRPhenomX and SEOBNRv4. The precessing extension allows for flexibility choosing the Euler angles of the time-dependent rotation between the co-precessing and the inertial reference systems, including the single spin NNLO and the double spin MSA PN descriptions present in other models, numerical integration of the orbit averaged spin evolution equations, different choices for the evolution of the orbital angular momentum norm and a simple approximation to the ringdown behaviour., Comment: 19 pages, 11 figures

We present IMRPhenomXPHM, a phenomenological frequency-domain model for the gravitational-wave signal emitted by quasi-circular precessing binary black holes, which incorporates multipoles beyond the dominant quadrupole in the precessing frame. The model is a precessing extension of IMRPhenomXHM (Garc\'ia-Quir\'os 2020), based on approximate maps between aligned-spin waveform modes in the co-precessing frame and precessing waveform modes in the inertial frame, which is commonly referred to as "twisting up" the non-precessing waveforms. IMRPhenomXPHM includes IMRPhenomXP as a special case, the restriction to the dominant quadrupole contribution in the co-precessing frame. We implement two alternative mappings, one based on a single-spin PN approximation, as used in IMRPhenomPv2 (Hannam 2013), and one based on the double-spin MSA approach (Chatziioannou 2017). We include a detailed discussion of conventions used in the description of precessing binaries and of all choices made in constructing the model. The computational cost of \phXPHM is further reduced by extending the interpolation technique of (C. Garc\'ia-Quir\'os 2020) to the Euler angles. The accuracy, speed, robustness and modularity of the IMRPhenomX family will make these models productive tools for gravitational wave astronomy in the current era of greatly increased number and diversity of detected events., Comment: Version accepted for publication in Physical Review D

In this paper we present IMRPhenomXAS, a thorough overhaul of the IMRPhenomD [1,2] waveform model, which describes the dominant $l=2, \:| m | = 2$ spherical harmonic mode of non-precessing coalescing black holes in terms of piecewise closed form expressions in the frequency domain. Improvements include in particular the accurate treatment of unequal spin effects, and the inclusion of extreme mass ratio waveforms. IMRPhenomD has previously been extended to approximately include spin precession [3] and subdominant spherical harmonics [4], and with its extensions it has become a standard tool in gravitational wave parameter estimation. Improved extensions of IMRPhenomXAS are discussed in companion papers [5,6]., Comment: 29 pages. 20 figures. Comments and feedback welcome! This paper corresponds to LIGO DCC P2000018

We present the IMRPhenomXHM frequency domain phenomenological waveform model for the inspiral, merger and ringdown of quasi-circular non-precessing black hole binaries. The model extends the IMRPhenomXAS waveform model, which describes the dominant quadrupole modes $\ell = |m| = 2$, to the harmonics $(\ell, |m|)=(2,1), (3,3), (3,2), (4,4)$, and includes mode mixing effects for the $(3,2)$ spherical harmonic. IMRPhenomXHM is calibrated against hybrid waveforms, which match an inspiral phase described by the effective-one-body model and post-Newtonian amplitudes for the subdominant harmonics to numerical relativity waveforms and numerical solutions to the perturbative Teukolsky equation for large mass ratios up to 1000. A computationally efficient implementation of the model is available as part of the LSC Algorithm Library Suite., Comment: 30 pages, 23 figures. Updated to match published version

We analyze a new numerical relativity dataset of spinning but nonprecessing binary black holes on eccentric orbits, with eccentricities from approximately $0.1$ to $0.5$, with dimensionless spins up to $0.75$ included at mass ratios $q=m_1/m_2 = (1, 2)$, and further nonspinning binaries at mass ratios $q = (1.5, 3, 4)$. A comparison of the final mass and spin of these simulations with noneccentric data extends previous results in the literature on circularization of eccentric binaries to the spinning case. For the $(l,m)=(2,2)$ spin-weighted spherical harmonic mode we construct eccentric hybrid waveforms that connect the numerical relativity data to a post-Newtonian description for the inspiral, and we discuss the limitations in the current knowledge about post-Newtonian theory which complicate the generation of eccentric hybrid waveforms. We also perform a Bayesian parameter estimation study, quantifying the parameter biases introduced when using three different quasicircular waveform models to estimate the parameters of highly eccentric binary systems. We find that the used aligned-spin quasicircular model including higher order modes produces lower bias in certain parameters than the nonprecessing quasicircular model without higher order modes and the quasicircular precessing model., Comment: Matching published version

For a Schwarzchild black hole of mass $M$, we consider a test particle falling from rest at infinity and becoming trapped, at late time, on the unstable circular orbit of radius $r=4GM/c^2$. When the particle is endowed with a small mass, $\mu\ll M$, it experiences an effective gravitational self-force, whose conservative piece shifts the critical value of the angular momentum and the frequency of the asymptotic circular orbit away from their geodesic values. By directly integrating the self-force along the orbit (ignoring radiative dissipation), we numerically calculate these shifts to $O(\mu/M)$. Our numerical values are found to be in agreement with estimates first made within the Effective One Body formalism, and with predictions of the first law of black-hole-binary mechanics (as applied to the asymptotic circular orbit). Our calculation is based on a time-domain integration of the Lorenz-gauge perturbation equations, and it is a first such calculation for an unbound orbit. We tackle several technical difficulties specific to unbound orbits, illustrating how these may be handled in more general cases of unbound motion. Our method paves the way to calculations of the self-force along hyperbolic-type scattering orbits. Such orbits can probe the two-body potential down to the "light ring", and could thus supply strong-field calibration data for eccentricity-dependent terms in the Effective One Body model of merging binaries., Comment: 29 pages, 6 figures

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress., Comment: White Paper for the COST action "Gravitational Waves, Black Holes, and Fundamental Physics", 272 pages, 12 figures; v4: updated references and author list. Overall improvements and corrections. To appear in Classical and Quantum Gravity

We present TEOBResumS, a new effective-one-body (EOB) waveform model for nonprecessing (spin-aligned) and tidally interacting compact binaries.Spin-orbit and spin-spin effects are blended together by making use of the concept of centrifugal EOB radius. The point-mass sector through merger and ringdown is informed by numerical relativity (NR) simulations of binary black holes (BBH) computed with the SpEC and BAM codes. An improved, NR-based phenomenological description of the postmerger waveform is developed.The tidal sector of TEOBResumS describes the dynamics of neutron star binaries up to merger and incorporates a resummed attractive potential motivated by recent advances in the post-Newtonian and gravitational self-force description of relativistic tidal interactions. Equation-of-state dependent self-spin interactions (monopole-quadrupole effects) are incorporated in the model using leading-order post-Newtonian results in a new expression of the centrifugal radius. TEOBResumS is compared to 135 SpEC and 19 BAM BBH waveforms. The maximum unfaithfulness to SpEC data $\bar{F}$ -- at design Advanced-LIGO sensitivity and evaluated with total mass $M$ varying between $10M_\odot \leq M \leq 200 M_\odot$ --is always below $2.5 \times 10^{-3}$ except for a single outlier that grazes the $7.1 \times 10^{-3}$ level. When compared to BAM data, $\bar{F}$ is smaller than $0.01$ except for a single outlier in one of the corners of the NR-covered parameter space, that reaches the $0.052$ level.TEOBResumS is also compatible, up to merger, to high end NR waveforms from binary neutron stars with spin effects and reduced initial eccentricity computed with the BAM and THC codes. The model is designed to generate accurate templates for the analysis of LIGO-Virgo data through merger and ringdown. We demonstrate its use by analyzing the publicly available data for GW150914., Comment: 39 pages, 36 figures. Extended appendix with discussion of the postmerger fits. Version accepted for publication in Phys. Rev. D

It is known that a near-extremal Kerr black hole can be spun up beyond its extremal limit by capturing a test particle. Here we show that overspinning is always averted once back-reaction from the particle's own gravity is properly taken into account. We focus on nonspinning, uncharged, massive particles thrown in along the equatorial plane, and work in the first-order self-force approximation (i.e., we include all relevant corrections to the particle's acceleration through linear order in the ratio, assumed small, between the particle's energy and the black hole's mass). Our calculation is a numerical implementation of a recent analysis by two of us [Phys.\ Rev.\ D {\bf 91}, 104024 (2015)], in which a necessary and sufficient "censorship" condition was formulated for the capture scenario, involving certain self-force quantities calculated on the one-parameter family of unstable circular geodesics in the extremal limit. The self-force information accounts both for radiative losses and for the finite-mass correction to the critical value of the impact parameter. Here we obtain the required self-force data, and present strong evidence to suggest that captured particles never drive the black hole beyond its extremal limit. We show, however, that, within our first-order self-force approximation, it is possible to reach the extremal limit with a suitable choice of initial orbital parameters. To rule out such a possibility would require (currently unavailable) information about higher-order self-force corrections., Comment: 13 pages, 3 figures

We study the scenario in which a massive particle is thrown into a rapidly rotating Kerr black hole in an attempt to spin it up beyond its extremal limit, challenging weak cosmic censorship. We work in black-hole perturbation theory, and focus on non-spinning, uncharged particles sent in on equatorial orbits. We first identify the complete parameter-space region in which overspinning occurs when back-reaction effects from the particle's self-gravity are ignored. We find, in particular, that overspinning can be achieved only with particles sent in from infinity. Gravitational self-force effects may prevent overspinning by radiating away a sufficient amount of the particle's angular momentum ("dissipative effect"), and/or by increasing the effective centrifugal repulsion, so that particles with suitable parameters never get captured ("conservative effect"). We analyze the full effect of the self-force, thereby completing previous studies by Jacobson and Sotiriou (who neglected the self-force) and by Barausse, Cardoso and Khanna (who considered the dissipative effect on a subset of orbits). Our main result is an inequality, involving certain self-force quantities, which describes a necessary and sufficient condition for the overspinning scenario to be overruled. This "censorship" condition is formulated on a certain one-parameter family of geodesics in an extremal Kerr geometry. We find that the censorship condition is insensitive to the dissipative effect (within the first-order self-force approximation used here), except for a subset of perfectly fine-tuned orbits, for which a separate censorship condition is derived. We do not obtain here the self-force input needed to evaluate either of our two conditions, but discuss the prospects for producing the necessary data using state-of-the-art numerical codes., Comment: 25 pages, 4 figures

Using the results of arXiv:0804.0009, where all timelike supersymmetric backgrounds of N=2, D=4 matter-coupled supergravity with Fayet-Iliopoulos gauging were classified, we construct genuine nut-charged BPS black holes in AdS_4 with nonconstant moduli. The calculations are exemplified for the SU(1,1)/U(1) model with prepotential F=-iX^0X^1. The resulting supersymmetric black holes have a hyperbolic horizon and carry two electric, two magnetic and one nut charge, which are however not all independent, but are given in terms of three free parameters. We find that turning on a nut charge lifts the flat directions in the effective black hole potential, such that the horizon values of the scalars are completely fixed by the charges. We also oxidize the solutions to eleven dimensions, and find that they generalize the geometry found in hep-th/0105250 corresponding to membranes wrapping holomorphic curves in a Calabi-Yau five-fold. Finally, a class of nut-charged Nernst branes is constructed as well, but these have curvature singularities at the horizon., Comment: 21 pages, no figures, uses JHEP3.cls