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.
The extreme-gravity collisions between black holes allow us to probe the underlying theory of gravity. We apply the theory-agnostic inspiral-merger-ringdown consistency test to an example theory beyond general relativity for the first time. Here we focus on the string-inspired Einstein-dilaton Gauss-Bonnet gravity and modify the inspiral, ringdown, and remnant black hole properties of the gravitational waveform. We found that future multiband observations allow us to constrain the theory stronger than current observations by an order of magnitude. The formalism developed here can easily be app…
Gravitational waves from extreme gravity events such as the coalescence of two black holes in a binary system fill our observable universe, bearing with them the underlying theory of gravity driving their process. One compelling alternative theory of gravity -- known as Einstein-dilaton Gauss-Bonnet gravity motivated by string theory -- describes the presence of an additional dilaton scalar field coupled directly to higher orders of the curvature, effectively describing a "fifth force" interaction and the emission of scalar dipole radiation between two scalarized black holes. Most previous stu…
An extreme mass ratio inspiral consists of two parts: adiabatic inspiral and plunge. The plunge trajectory from the innermost stable circular orbit (ISCO) is special (somewhat independent of initial conditions). We write an expression for its solution in closed-form and for the emitted waveform. In particular we extract an expression for the associated black-hole ringdown amplitudes, and evaluate them numerically.
The inspiral-merger-ringdown (IMR) consistency test checks the consistency of the final mass and final spin of a binary black hole merger remnant, independently inferred via the inspiral and merger-ringdown parts of the waveform. As binaries are expected to be nearly circularized when entering the frequency band of ground-based detectors, tests of general relativity (GR) currently employ quasicircular waveforms. We quantify the effect of residual orbital eccentricity on the IMR consistency test. We find that eccentricity causes a significant systematic bias in the inferred final mass and spin …
We analyze the problem of parameter estimation for compact binary systems that could be detected by ground-based gravitational wave detectors. So far this problem has only been dealt with for the inspiral and the ringdown phases separately. In this paper, we combine the information from both signals, and we study the improvement in parameter estimation, at a fixed signal-to-noise ratio, by including the ringdown signal without making any assumption on the merger phase. The study is performed for both initial and advanced LIGO and VIRGO detectors.
We investigate the capability of LISA to measure the sky position of equal-mass, nonspinning black hole binaries, combining for the first time the entire inspiral-merger-ringdown signal, the effect of the LISA orbits, and the complete three-channel LISA response. We consider an ensemble of systems near the peak of LISA's sensitivity band, with total rest mass of 2\times10^6 M\odot, a redshift of z = 1, and randomly chosen orientations and sky positions. We find median sky localization errors of approximately \sim3 arcminutes. This is comparable to the field of view of powerful electromagnetic …
Current tests of General Relativity are performed using approximations which neglect a key feature of complete solution of Einstein's theory: higher-order modes. Our analysis will reassess these tests, including these higher-order mode effects. We have chosen to perform inspiral-merger-ringdown consistency tests on the gravitational transients detected by LIGO and Virgo during the observing run O2. We use an approximant which includes all higher modes with $\ell \le 4$ (NRSur7dq2) and then, for the most interesting cases, we repeat the tests involving fits on Numerical Relativity simulations.
Spherical harmonic modes of gravitational waveforms for inspiraling compact binaries in eccentric orbits from post-Newtonian (PN) theory accurate to third post-Newtonian order, and those extracted from numerical relativity (NR) simulations for binary black holes (BBHs) are compared. We combine results from the two approaches (PN and NR) to construct time-domain hybrid waveforms that describe the complete evolution of BBH mergers through inspiral-merger-ringdown (IMR) stages. These hybrids are then used in constructing a fully analytical dominant mode ($\ell$=2, $|m|$=2) eccentric IMR model. A …
We present an analytical waveform family describing gravitational waves (GWs) from the inspiral, merger and ringdown of non-spinning black-hole binaries including the effect of several non-quadrupole modes [($\ell = 2, m = \pm 1), (\ell = 3, m = \pm 3), (\ell = 4, m = \pm 4)$ apart from $(\ell = 2, m=\pm2)$]. We first construct spin-weighted spherical harmonics modes of hybrid waveforms by matching numerical-relativity simulations (with mass ratio $1-10$) describing the late inspiral, merger and ringdown of the binary with post-Newtonian/effective-one-body waveforms describing the early inspir…
Searches for gravitational waves (GWs) from binary black holes using interferometric GW detectors require the construction of template banks for performing matched filtering while analyzing the data. Placement of templates over the parameter space of binaries, as well as coincidence tests of GW triggers from multiple detectors make use of the definition of a metric over the space of gravitational waveforms. Although recent searches have employed waveform templates coherently describing the inspiral, merger and ringdown (IMR) of the coalescence, the metric used in the template banks and coincid…
We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with non-precessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime,…
This paper presents an algorithm to accelerate the evaluation of inspiral-merger-ringdown waveform models for gravitational wave data analysis. While the idea can also be applied in the time domain, here we focus on the frequency domain, which is most typically used to reduced computational cost in gravitational wave data analysis. Our work extends the idea of multibanding, which has been developed to accelerate frequency domain waveforms, to include the merger and ringdown and spherical harmonics beyond the dominant quadrupole spherical harmonic. The original method is based on a heuristic al…
We numerically solve the Teukolsky equation in the time domain to obtain the gravitational-wave emission of a small mass inspiraling and plunging into the equatorial plane of a Kerr black hole. We account for the dissipation of orbital energy using the Teukolsky frequency-domain gravitational-wave fluxes for circular, equatorial orbits, down to the light-ring. We consider Kerr spins $-0.99 \leq q \leq 0.99$, and compute the inspiral-merger-ringdown (2,2), (2,1), (3,3), (3,2), (4,4), and (5,5) modes. We study the large-spin regime, and find a great simplicity in the merger waveforms, thanks to …
We develop a waveform model to describe the inspiral, merger and ringdown of binary systems with comparable and intermediate mass-ratios. This model incorporates first-order conservative self-force corrections to the energy and angular momentum, which are valid in the strong-field regime [1]. We model the radiative part of the self-force by deriving second-order radiative corrections to the energy flux. These corrections are obtained by minimizing the phase discrepancy between our self-force model and the effective one body model [2, 3] for a variety of mass-ratios. We show that our model perf…
We present fully general relativistic simulations of the quasi-circular inspiral and merger of charged, non-spinning, binary black holes with charge-to-mass ratio $λ\le 0.3$. We discuss the key features that enabled long term and stable evolutions of these binaries. We also present a formalism for computing the angular momentum carried away by electromagnetic waves, and the electromagnetic contribution to black-hole horizon properties. We implement our formalism and present the results for the first time in numerical-relativity simulations. In addition, we compare our full non-linear solutions…
We describe a general procedure to generate spinning, precessing waveforms that include inspiral, merger and ringdown stages in the effective-one-body (EOB) approach. The procedure uses a precessing frame in which precession-induced amplitude and phase modulations are minimized, and an inertial frame, aligned with the spin of the final black hole, in which we carry out the matching of the inspiral-plunge to merger-ringdown waveforms. As a first application, we build spinning, precessing EOB waveforms for the gravitational modes l=2 such that in the nonprecessing limit those waveforms agree wit…
The first spectral numerical simulations of 16 orbits, merger, and ringdown of an equal-mass non-spinning binary black hole system are presented. Gravitational waveforms from these simulations have accumulated numerical phase errors through ringdown of ~0.1 radian when measured from the beginning of the simulation, and ~0.02 radian when waveforms are time and phase shifted to agree at the peak amplitude. The waveform seen by an observer at infinity is determined from waveforms computed at finite radii by an extrapolation process accurate to ~0.01 radian in phase. The phase difference between t…
Modeling the merger-ringdown of an eccentric test-mass inspiral into a Kerr black hole using the effective-one-body framework
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；University of Maryland（马里兰大学）；Niels Bohr Institute（尼尔斯·玻尔研究所）；University of Rhode Island（罗德岛大学）；University of Massachusetts, Dartmouth（马萨诸塞大学达特茅斯分校）
We discuss a new ringdown frequency mode for vacuum perturbations of the Kerr black hole. We evolve initial data for the vacuum radial Teukolsky equation using a near horizon approximation, and find a frequency mode analogous to that found in a recent study of radiation generated by a plunging particle close to the Kerr horizon. We discuss our results in the context of that study. We also explore the utility of this mode by fitting a numerical waveform with a combination of the usual quasi-normal modes (QNMs) and the new oscillation frequency.
Advanced LIGO's recent observations of gravitational waves (GWs) from merging binary black holes have opened up a unique laboratory to test general relativity (GR) in the highly relativistic regime. One of the tests used to establish the consistency of the first LIGO event with a binary black hole merger predicted by GR was the inspiral-merger-ringdown consistency test. This involves inferring the mass and spin of the remnant black hole from the inspiral (low-frequency) part of the observed signal and checking for the consistency of the inferred parameters with the same estimated from the post…
We present exact solutions of test particle orbits spiralling inward from the innermost stable circular orbit (ISCO) of a Kerr black hole. Our results are valid for any allowed value of the angular momentum $a$-parameter of the Kerr metric. These solutions are of considerable physical interest. In particular, the radial 4-velocity of these orbits is both remarkably simple and, with the radial coordinate scaled by its ISCO value, universal in form, otherwise completely independent of the black hole spin.
We present a prescription for computing gravitational waveforms for the inspiral, merger and ringdown of non-spinning eccentric binary black hole systems. The inspiral waveform is computed using the post-Newtonian expansion and the merger waveform is computed by interpolating a small number of quasi-circular NR waveforms. The use of circular merger waveforms is possible because eccentric binaries circularize in the last few cycles before the merger, which we demonstrate up to mass ratio $q = m_1/m_2 = 3$. The complete model is calibrated to 23 numerical relativity (NR) simulations starting ~20…
We estimate the expected signal-to-noise ratios (SNRs) from the three phases (inspiral,merger,ringdown) of coalescing binary black holes (BBHs) for initial and advanced ground-based interferometers (LIGO/VIRGO) and for space-based interferometers (LISA). LIGO/VIRGO can do moderate SNR (a few tens), moderate accuracy studies of BBH coalescences in the mass range of a few to about 2000 solar masses; LISA can do high SNR (of order 10^4) high accuracy studies in the mass range of about 10^5 to 10^8 solar masses. BBHs might well be the first sources detected by LIGO/VIRGO: they are visible to much …
The waveforms from binary black hole mergers include inspiral, merger, and ringdown parts. Usually, the inspiral waveform can be obtained by calibrating from post-Newtonian approximation; The merger and ringdown ones can be gotten from the quasinormal modes with black hole perturbation theory. However, for more general black holes, the calculation of the quasinormal modes is not trivial. In this paper we use the photon sphere to get the quasinormal modes of spinning black holes. Then we connect the ringdown wave with the inspiral part to get full waveforms and compare with the ones from numeri…
We study the inspiral, merger and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and Post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the Post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the Post-Newtonian series to the numerical results is non-monotonic. …
Future space-borne interferometers will be able to detect gravitational waves at $10^{-3}$ to $10^{-1}$ Hz. At this band extreme-mass-ratio inspirals (EMRIs) can be promising gravitational wave sources. In this paper, we investigate possibility of testing Kerr hypothesis against a parametrized non-Kerr metric by matching EMRI signals. However, EMRIs from either equatorial orbits or inclined orbits suffer from the "confusion problem". Our results show that, within the time scale before radiation flux plays an important role, small and moderate deviations from the Kerr spacetime($|δ_i|<1$) can b…
ESIGMAHM: An Eccentric, Spinning inspiral-merger-ringdown waveform model with Higher Modes for the detection and characterization of binary black holes
We investigate resonance crossings of a charged body moving around a Kerr black hole immersed in an external homogeneous magnetic field. This system can serve as an electromagnetic analogue of a weakly non-integrable extreme mass ratio inspiral (EMRI). In particular, the presence of the magnetic field renders the conservative part of the system non-integrable in the Liouville sense, while the electromagnetic self-force causes the charged body to inspiral. By studying the system without the self-force, we show the existence of an approximate Carter-like constant and discuss how resonances grow …
Gravitational-wave signals from black-hole binaries with non-precessing spins are described by four parameters -- each black hole's mass and spin. It has been shown that the dominant spin effects can be modeled by a \emph{single} spin parameter, leading to the development of several \emph{three-parameter} waveform models. Previous studies indicate that these models should be adequate for gravitational-wave detection. In this paper we focus on the systematic biases that would result from using them to estimate binary parameters, and consider a one-parameter family of configurations at one choic…
The LIGO/Virgo detections of binary black hole mergers marked a watershed moment in astronomy, ushering in the era of precision tests of Kerr dynamics. We review theoretical and experimental challenges that must be overcome to carry out black hole spectroscopy with present and future gravitational wave detectors. Among other topics, we discuss quasinormal mode excitation in binary mergers, astrophysical event rates, tests of black hole dynamics in modified theories of gravity, parameterized "post-Kerr" ringdown tests, exotic compact objects, and proposed data analysis methods to improve spectr…
Biases in Ringdown Tests of General Relativity from Gravitational-Wave Microlensing
Indian Association for the Cultivation of Science（印度科学培养协会）；The Inter-University Centre for Astronomy and Astrophysics (IUCAA)（大学间天文学与天体物理中心）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）
We first use five non-spinning and two mildly spinning (chi_i \simeq -0.44, +0.44) numerical-relativity waveforms of black-hole binaries and calibrate an effective-one-body (EOB) model for non-precessing spinning binaries, notably its dynamics and the dominant (2,2) gravitational-wave mode. Then, we combine the above results with recent outcomes of small-mass-ratio simulations produced by the Teukolsky equation and build a prototype EOB model for detection purposes, which is capable of generating inspiral-merger-ringdown waveforms for non-precessing spinning black-hole binaries with any mass r…
Exact Cancellation of Horizon Modes in Kerr Ringdown
Institute for Cosmic Ray Research, The University of Tokyo（宇宙射线研究所，东京大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Department of Physics, Tokyo Metropolitan University（东京都立大学物理系）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（宇宙早期研究中心（RESCEU），东京大学理学研究科）
The space based interferometer LISA will be capable of detecting the gravitational waves emitted by stellar mass black holes or neutron stars slowly inspiralling into the supermassive black holes found in the centre of most galaxies. The gravitational wave signal from such an extreme mass ratio inspiral (EMRI) event will provide a unique opportunity to test whether the spacetime metric around the central black hole is well described by the Kerr solution. In this paper a well studied model for EMRIs around Kerr black holes is extended to a family of parametrically deformed bumpy black holes whi…
The gravitational wave observations of colliding black holes have opened a new window into the unexplored extreme gravity sector of physics, where the gravitational fields are immensely strong, non-linear, and dynamical. 10 binary black hole merger events observed so far can be used to test Einstein's theory of general relativity, which has otherwise been proven to agree with observations from several sources in the weak- or static-field regimes. One interesting future possibility is to detect gravitational waves from GW150914-like stellar-mass black hole binaries with both ground-based and sp…
Spinning Effective-to-Backwards One Body ($\texttt{SEBOB}$): combining Effective One-Body inspirals and Backwards One-Body merger-ringdowns for aligned spin black hole binaries
The final stage of a binary black hole merger is ringdown, in which the system is described by a Kerr black hole with quasinormal mode perturbations. It is far from straightforward to identify the time at which the ringdown begins. Yet determining this time is important for precision tests of the general theory of relativity that compare an observed signal with quasinormal mode descriptions of the ringdown, such as tests of the no-hair theorem. We present an algorithmic method to analyze the choice of ringdown start time in the observed waveform. This method is based on determining how close t…
