Testing general relativity with gravitational waves: An overview

The detections of gravitational-wave (GW) signals from compact binary coalescence by ground-based detectors have opened up the era of GW astronomy. These observations provide opportunities to test Einstein's general theory of relativity at the strong-field regime. Here we give a brief overview of the various GW-based tests of General Relativity (GR) performed by the LIGO-Virgo collaboration on the detected GW events to date. After providing details for the tests performed in four categories, we discuss the prospects for each test in the context of future GW detectors. The four categories of tests include the consistency tests, parametrized tests for GW generation and propagation, tests for the merger remnant properties, and GW polarization tests.Comment: 21 pages, 7 figures, review article contributed as part of the Special Issue on Current and Future Tests of General Relativity of the journal Univers

Inconsistent black hole kick estimates from gravitational-wave models

The accuracy of gravitational-wave models of compact binaries has traditionally been addressed by the mismatch between the model and numerical-relativity simulations. This is a measure of the overall agreement between the two waveforms. However, the largest modelling error typically appears in the strong-field merger regime and may affect subdominant signal harmonics more strongly. These inaccuracies are often not well characterised by the mismatch. We explore the use of a complementary, physically motivated tool to investigate the accuracy of gravitational-wave harmonics in waveform models: the remnant's recoil, or kick velocity. Asymmetric binary mergers produce remnants with significant recoil, encoded by subtle imprints in the gravitational-wave signal. The kick estimate is highly sensitive to the intrinsic inaccuracies of the modelled gravitational-wave harmonics during the strongly relativistic merger regime. Here we investigate the accuracy of the higher harmonics in four state-of-the-art waveform models of binary black holes. We find that the SEOBNRv4HM_ROM, IMRPhenomHM, IMRPhenomXHM and NRHybSur3dq8 models are not consistent in their kick predictions. Our results enable us to identify regions in the parameter space where the models require further improvement and support the use of the kick estimate to investigate waveform systematics. We discuss how numerical-relativity kick estimates could be used to calibrate waveform models further, proposing the first steps towards kick-based gravitational-wave tuning

Black-hole kicks: a tool to measure the accuracy of gravitational-wave models

Asymmetric binary systems radiate linear momentum through gravitational waves, leading to the recoil of the merger remnant. Black-hole kicks have attracted much attention because of their astrophysical implications. However, little information can be extracted from the observations made by LIGO and Virgo so far. In this work, we discuss how the gravitational recoil, an effect that is encoded in the gravitational signal, can be used to test the accuracy of waveform models. Gravitational-wave models of merging binary systems have become fundamental to detect potential signals and infer the parameters of observed sources. But, as the interferometers' sensitivity is enhanced in current and future detectors, gravitational waveform models will have to be further improved. We find that the kick is highly sensitive to waveform inaccuracies and can therefore be a useful diagnostic test. Furthermore, we observe that current higher-mode waveform models are not consistent in their kick predictions. For this reason, we discuss whether measuring and improving waveform accuracy can, in turn, allow us to extract meaningful information about the kick in future observations

Intrinsic and extrinsic geometries of a tidally deformed black hole

A description of the event horizon of a perturbed Schwarzschild black hole is provided in terms of the intrinsic and extrinsic geometries of the null hypersurface. This description relies on a Gauss-Codazzi theory of null hypersurfaces embedded in spacetime, which extends the standard theory of spacelike and timelike hypersurfaces involving the first and second fundamental forms. We show that the intrinsic geometry of the event horizon is invariant under a reparameterization of the null generators, and that the extrinsic geometry depends on the parameterization. Stated differently, we show that while the extrinsic geometry depends on the choice of gauge, the intrinsic geometry is gauge invariant. We apply the formalism to solutions to the vacuum field equations that describe a tidally deformed black hole. In a first instance we consider a slowly-varying, quadrupolar tidal field imposed on the black hole, and in a second instance we examine the tide raised during a close parabolic encounter between the black hole and a small orbiting body.Comment: 27 pages, 4 figure

Training Strategies for Deep Learning Gravitational-Wave Searches

Compact binary systems emit gravitational radiation which is potentially detectable by current Earth bound detectors. Extracting these signals from the instruments' background noise is a complex problem and the computational cost of most current searches depends on the complexity of the source model. Deep learning may be capable of finding signals where current algorithms hit computational limits. Here we restrict our analysis to signals from non-spinning binary black holes and systematically test different strategies by which training data is presented to the networks. To assess the impact of the training strategies, we re-analyze the first published networks and directly compare them to an equivalent matched-filter search. We find that the deep learning algorithms can generalize low signal-to-noise ratio (SNR) signals to high SNR ones but not vice versa. As such, it is not beneficial to provide high SNR signals during training, and fastest convergence is achieved when low SNR samples are provided early on. During testing we found that the networks are sometimes unable to recover any signals when a false alarm probability $<10^{-3}$ is required. We resolve this restriction by applying a modification we call unbounded Softmax replacement (USR) after training. With this alteration we find that the machine learning search retains $\geq 97.5\%$ of the sensitivity of the matched-filter search down to a false-alarm rate of 1 per month

Finite tidal effects in GW170817: observational evidence or model assumptions?

After the detection of gravitational waves caused by the coalescence of compact objects in the mass range of neutron stars, GW170817, several studies have searched for an imprint of tidal effects in the signal, employing different model assumptions. One important distinction is whether or not to assume that both objects are neutron stars and obey the same equation of state. Some studies assumed independent properties. Others assume a universal equation of state, and in addition that the tidal deformability follows certain phenomenological relations. An important question is whether the gravitational-wave data alone constitute observational evidence for finite tidal effects. All studies provide Bayesian credible intervals, often without sufficiently discussing the impact of prior assumptions, especially in the case of lower limits on the neutron-star tidal deformability or radius. In this article, we scrutinize the implicit and explicit prior assumptions made in those studies. Our findings strongly indicate that existing lower credible bounds are mainly a consequence of prior assumptions combined with information gained about the system's masses. Importantly, those lower bounds are typically not informed by the observation of tidal effects in the gravitational-wave signal. Thus, regarding them as observational evidence might be misleading without a more detailed discussion. Further, we point out technical problems and conceptual inconsistencies in existing studies. We also assess the limitations due to systematic waveform model uncertainties in a novel way, demonstrating that differences between existing models are not guaranteed to be small enough for an unbiased estimation of lower bounds on the tidal deformability. Finally, we propose strategies for gravitational-wave data analysis designed to avoid some of the problems we uncovered