arXiv subjects

Gaurav Khanna

Publications and source records attributed to Gaurav Khanna.

At least 73 records · Page 4Linked to original sources

arXiv2017

Black Hole Spectroscopy: Systematic Errors and Ringdown Energy Estimates

The relaxation of a distorted black hole to its final state provides important tests of general relativity within the reach of current and upcoming gravitational wave facilities. In black hole perturbation theory, this phase consists of a simple linear superposition of exponentially damped sinusoids (the quasinormal modes) and of a power-law tail. How many quasinormal modes are necessary to describe waveforms with a prescribed precision? What error do we incur by only including quasinormal modes, and not tails? What other systematic effects are present in current state-of-the-art numerical waveforms? These issues, which are basic to testing fundamental physics with distorted black holes, have hardly been addressed in the literature. We use numerical relativity waveforms and accurate evolutions within black hole perturbation theory to provide some answers. We show that (i) a determination of the fundamental $l=m=2$ quasinormal mode to within $1\%$ or better requires the inclusion of at least the first overtone, and preferably of the first two or three overtones; (ii) a determination of the black hole mass and spin with precision better than $1\%$ requires the inclusion of at least two quasinormal modes for any given angular harmonic mode $(\ell,\,m)$. We also improve on previous estimates and fits for the ringdown energy radiated in the various multipoles. These results are important to quantify theoretical (as opposed to instrumental) limits in parameter estimation accuracy and tests of general relativity allowed by ringdown measurements with high signal-to-noise ratio gravitational wave detectors.

gr-qc↗

arXiv2017

Scalar collapse in AdS with an OpenCL open source code

We study the spherically symmetric collapse of a scalar field in anti-de Sitter spacetime using a newly constructed, open-source code which parallelizes over heterogeneous architectures using the open standard OpenCL. An open question for this scenario concerns how to tell, a priori, whether some form of initial data will be stable or will instead develop under the turbulent instability into a black hole in the limit of vanishing amplitude. Previous work suggested the existence of islands of stability around quasiperiodic solutions, and we use this new code to examine the stability properties of approximately quasiperiodic solutions which balance energy transfer to higher modes with energy transfer to lower modes. The evolutions provide some evidence, though not conclusively, for stability of initial data sufficiently close to quasiperiodic solutions.

gr-qc↗

arXiv2017

Linearized Stability of Extreme Black Holes

Extreme black holes have been argued to be unstable, in the sense that under linearized gravitational perturbations of the extreme Kerr spacetime the Weyl scalar $ψ_4$ blows up along their event horizons at very late advanced times. We show numerically, by solving the Teukolsky equation in 2+1D, that all algebraically-independent curvature scalar polynomials approach limits that exist when advanced time along the event horizon approaches infinity. Therefore, the horizons of extreme black holes are stable against linearized gravitational perturbations. We argue that the divergence of $ψ_4$ is a consequence of the choice of a fixed tetrad, and that in a suitable dynamical tetrad all Weyl scalars, including $ψ_4$, approach their background extreme Kerr values. We make similar conclusions also for the case of scalar field perturbations of extreme Kerr.

gr-qc↗

arXiv2017

Gravitational wave sources: reflections and echoes

The recent detection of gravitational waves has generated interest in alternatives to the black hole interpretation of sources. One set of such alternatives involves a prediction of gravitational wave "echoes". We consider two aspects of possible echoes: First, general features of echoes coming from spacetime reflecting conditions. We find that the detailed nature of such echoes does not bear any clear relationship to quasi-normal frequencies. Second, we point out the pitfalls in the analysis of local reflecting "walls" near the horizon of rapidly rotating black holes.

gr-qc↗

arXiv2017

Scalar Fields in Black Hole Spacetimes

The time-evolution of matter fields in black hole exterior spacetimes is a well-studied subject, spanning several decades of research. However, the behavior of fields in the black hole interior spacetime, has only relatively recently begun receiving some attention from the research community. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, including the black hole interior. We recover the expected late-time power-law "tails" on the exterior (null infinity, time-like infinity and the horizon). In the interior region, we find an interesting oscillatory behavior that is characterized by the multipole index $\ell$ of the scalar field. In addition, we also study the extremal Kerr case and find strong indications of an instability developing at the horizon.

gr-qc↗

arXiv2017

Black Hole Ringing, Quasinormal Modes, and Light Rings

Modelling of gravitational waves from binary black hole inspiral has played an important role in the recent observations of such signals. The late-stage ringdown phase of the gravitational waveform is often associated with the null particle orbit ("light ring") of the black hole spacetime. With simple models we show that this link between the light ring and spacetime ringing is based more on the history of specific models than on an actual constraining relationship. We also show, in particular, that a better understanding of the dissociation of the two may be relevant to the astrophysically interesting case of rotating (Kerr) black holes.

gr-qc↗

arXiv2016

Arrival Times of Gravitational Radiation Peaks for Binary Inspiral

Modeling of gravitational waves (GWs) from binary black hole inspiral brings together early post-Newtonian waveforms and late quasinormal ringing waveforms. Attempts to bridge the two limits without recourse to numerical relativity involve predicting the time of the peak GW amplitude. This prediction will require solving the question of why the peak of the "source," i.e., the peak of the binary angular velocity, does not correspond to the peak of the GW amplitude. We show here that this offset can be understood as due to the existence two distinct components of the radiation: the "direct" radiation analogous to that in flat spacetime, and "scattered" radiation associated with curved spacetime. The time dependence of these two components, and of their relative phases determines the location of the peak amplitude. We use a highly simplified model to clarify the twocomponent nature of the source, then demonstrate that the explanation is valid also for an extreme mass ratio binary inspiral.

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arXiv2016

Gravitational waves from a plunge into a nearly extremal Kerr black hole

We study numerically in the time domain the linearized gravitational waves emitted from a plunge into a nearly extremal Kerr black hole by solving the inhomogeneous Teukolsky equation. We consider spinning black holes for which the specific spin angular momentum $a/M=1-ε$, and we consider values of $ε\geq 10^{-6}$. We find an effective transient behavior for the quasi-normal ringdown: the early phase of the quasi-normal ringdown is governed by a decay according to inverse time, with frequency equaling twice the black hole's horizon frequency. The smaller $ε$ the later the transition from this transient inverse time decay to exponential decay. Such sources, if exist, may be interesting potential sources for terrestrial or space borne gravitational wave observatories.

gr-qc↗

arXiv2016

Scientific Computing Using Consumer Video-Gaming Hardware Devices

Commodity video-gaming hardware (consoles, graphics cards, tablets, etc.) performance has been advancing at a rapid pace owing to strong consumer demand and stiff market competition. Gaming hardware devices are currently amongst the most powerful and cost-effective computational technologies available in quantity. In this article, we evaluate a sample of current generation video-gaming hardware devices for scientific computing and compare their performance with specialized supercomputing general purpose graphics processing units (GPGPUs). We use the OpenCL SHOC benchmark suite, which is a measure of the performance of compute hardware on various different scientific application kernels, and also a popular public distributed computing application, Einstein@Home in the field of gravitational physics for the purposes of this evaluation.

physics.comp-ph↗

arXiv2016

Black hole binary inspiral: Analysis of the plunge

Binary black hole coalescence has its peak of gravitational wave generation during the "plunge," the transition from quasicircular early motion to late quasinormal ringing. Although advances in numerical relativity have provided plunge waveforms, there is still no intuitive or phenomenological understanding of plungecomparable to that of the early and late stages. Here we make progress in developing such understanding by focusing on the excitation of quasinormal ringing (QNR) during the plunge. We rely on insights of the linear mathematics of the particle perturbation model for the extreme mass limit. Our analysis, based on the Fourier domain Green function, and a simple initial model, point to the crucial role played by the kinematics near the "light ring" (the circular photon orbit) in determining the excitation of QNR. That insight is then shown to successfully explain Schwarzschild QNR found with evolution codes. Lastly, a phenomenological explanation is given for the underlying importance of the light ring.

gr-qc↗

arXiv2015

Self-force gravitational waveforms for extreme and intermediate mass ratio inspirals. III: Spin-orbit coupling revisited

The first- and second-order dissipative self force and the first order conservative self force are applied together with spin-orbit coupling to the quasi-circular motion of a test mass in the spacetime of a Schwarzschild black hole, for extreme or intermediate mass ratios. The partial dephasing of the gravitational waveform (at the order that is independent of the system's mass ratio) due to the self force is compared with that of spin-orbit coupling. We find that accurate waveforms for parameter estimation need to include both effects. Specifically, we find a particular value for the spin parameter such that the spin-orbit effect cancels out the self-force effect on the waveform. Exclusion of dephasing effects that are independent of the mass ratio therefore might lead to a non-perturbative error in the estimation of the system's parameters.

gr-qc↗

arXiv2015

Brief note on high-multipole Kerr tails

In this note we reconsider the late-time, power-law decay rate of scalar fields in a Kerr space-time background. We implement a number of mathematical and computational enhancements to our time-domain, (2+1)D Teukolsky evolution code and are able to obtain reliable decay rates for multipoles as high as $\ell=16$. Our numerical results suggest full agreement with the proposed decay expressions in recent work for both the finite distance, and null infinity cases. We also study the same in the context of extremal Kerr space-time and find that the same results hold, except that the horizon tails follow the null infinity expressions instead.

gr-qc↗

arXiv2015

Black holes in anti-de Sitter: quasinormal modes, tails and tales of flat spacetime

Black holes in asymptotically anti-de Sitter (AdS) spacetimes have been the subject of intense scrutiny, including detailed frequency-domain analysis and full nonlinear evolutions. Remarkably, studies of linearized perturbations in the time-domain are scarce or non-existing. We close this gap by evolving linearized scalar wavepackets in the background of rotating BHs in AdS spacetimes. Our results show a number of interesting features. Small BHs in AdS behave as asymptotically flat BHs for early/intermediate times, displaying the same ringdown modes and power-law tails. As the field bounces back and forth between the horizon and the timelike boundary it "thermalizes" and the modes of AdS settle in. Finally, we have indications that wavepackets in the vicinity of fastly spinning BHs grow exponentially in time, signalling a superradiant instability of the geometry previously reported through a frequency-domain analysis.

gr-qc↗

arXiv2014

Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms

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 the extremely circular character of the plunging orbits. We also quantitatively examine the mixing of quasinormal modes during the ringdown, which induces complicated amplitude and frequency modulations in the waveforms. Finally, we explain how the study of small mass-ratio black-hole binaries helps extending effective-one-body models for comparable-mass, spinning black-hole binaries to any mass ratio and spin magnitude.

gr-qc↗

arXiv2014

Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed "splitting". We discuss far-field "splitting" in the full field and near-horizon "splitting" in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the "splitting" behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field "splitting" is explained by competition between projected modes. The near-horizon "splitting" is due to excitation of lower multipole modes that back excite the multipole mode for which "splitting" is observed. In both cases "splitting" is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter--mode excitation effect that we study.

gr-qc↗

arXiv2013

Mode coupling mechanism for late-time Kerr tails

We consider the decay rate for scalar fields in Kerr spacetime. We consider pure initial (azimuthal) multipoles $\ell'$ with respect to the class which includes Boyer-Lindquist coordinates, and focus attention on the decay rate of the multipole $\ell$. We use an iterative method proposed by Gleiser, Price, and Pullin, and identify the mode coupling mechanism through the iterations in powers of the square of the Kerr black hole's specific angular momentum that gives rise to a decay rate formula recently proposed by Zenginoğlu, Khanna, and Burko. Modes $\ell$ may be excited through different channels, each leading to its own decay rate. The asymptotic decay rate of the mode $\ell$ is the slowest of the decay rate of the various channels. In some cases, more than one channel leads to the same decay rate, and then the amplitude of the mode is the sum of the amplitudes of the partial fields generated by the individual channels. We also show that one may identify the asymptotically-dominant channel of mode excitations, and obtain approximate results for the mode of interest by studying the dominant channel. The results of the dominant channel approximation approach the full-mode results at late times, and their difference approaches zero quadratically in inverse time.

gr-qc↗

arXiv2013

Self-force gravitational waveforms for extreme and intermediate mass ratio inspirals. II: Importance of the second-order dissipative effect

We consider the importance of the second-order dissipative self force for gravitational wave dephasing for an extreme or intermediate mass ratio system moving along a quasi-circular Schwarzschild orbit. For the first-order self force we use the fully relativistic force in the Lorenz gauge for eternally circular geodesics. The second-order self force is modeled by its 3.5 post Newtonian counterpart. We evolve the system using the osculating orbits method, and obtain the gravitational waveforms, whose phase includes all the terms - within our approximation (and using the self force along circular geodesics) - that are independent of the system's mass ratio. The partial dephasing due to the second-order dissipative self force is substantially smaller than that of the first-order conservative self force, although they are both at the same order in the mass ratio.

gr-qc↗

arXiv2013

Black hole binary inspiral and trajectory dominance

Gravitational waves emitted during the inspiral, plunge and merger of a black hole binary carry linear momentum. This results in an astrophysically important recoil to the final merged black hole, a ``kick'' that can eject it from the nucleus of a galaxy. In a previous paper we showed that the puzzling partial cancellation of an early kick by a late antikick, and the dependence of the cancellation on black hole spin, can be understood from the phenomenology of the linear momentum waveforms. Here we connect that phenomenology to its underlying cause, the spin-dependence of the inspiral trajectories. This insight suggests that the details of plunge can be understood more broadly with a focus on inspiral trajectories.

gr-qc↗