arXiv subjects

Gaurav Khanna

Publications and source records attributed to Gaurav Khanna.

At least 91 records · Page 5Linked to original sources

arXiv2013

Modeling the horizon-absorbed gravitational flux for equatorial-circular orbits in Kerr spacetime

We propose an improved analytical model for the horizon-absorbed gravitational-wave energy flux of a small body in circular orbit in the equatorial plane of a Kerr black hole. Post-Newtonian (PN) theory provides an analytical description of the multipolar components of the absorption flux through Taylor expansions in the orbital frequency. Building on previous work, we construct a mode-by-mode factorization of the absorbed flux whose Taylor expansion agrees with current PN results. This factorized form significantly improves the agreement with numerical results obtained with a frequency-domain Teukolsky code, which evolves through a sequence of circular orbits up to the photon orbit. We perform the comparison between model and numerical data for dimensionless Kerr spins $-0.99 \leq q \leq 0.99$ and for frequencies up to the light ring of the Kerr black hole. Our proposed model enforces the presence of a zero in the flux at an orbital frequency equal to the frequency of the horizon, as predicted by perturbation theory. It also reproduces the expected divergence of the flux close to the light ring. Neither of these features are captured by the Taylor-expanded PN flux. Our proposed absorption flux can also help improve models for the inspiral, merger, ringdown of small mass-ratio binary systems.

gr-qc↗

arXiv2012

High Accuracy Gravitational Waveforms from Black Hole Binary Inspirals Using OpenCL

There is a strong need for high-accuracy and efficient modeling of extreme-mass-ratio binary black hole systems because these are strong sources of gravitational waves that would be detected by future observatories. In this article, we present sample results from our Teukolsky EMRI code: a time-domain Teukolsky equation solver (a linear, hyperbolic, partial differential equation solver using finite-differencing), that takes advantage of several mathematical and computational enhancements to efficiently generate long-duration and high-accuracy EMRI waveforms. We emphasize here the computational advances made in the context of this code. Currently there is considerable interest in making use of many-core processor architectures, such as Nvidia and AMD graphics processing units (GPUs) for scientific computing. Our code uses the Open Computing Language (OpenCL) for taking advantage of the massive parallelism offered by modern GPU architectures. We present the performance of our Teukolsky EMRI code on multiple modern processor architectures and demonstrate the high level of accuracy and performance it is able to achieve. We also present the code's scaling performance on a large supercomputer i.e. NSF's XSEDE resource: Keeneland (a 201 TeraFLOP/s, 120-node HP SL390 system with 240 Intel Xeon 5660 CPUs and 360 NVIDIA Fermi M2070 graphics processors, with the nodes connected by an InfiniBand QDR network).

gr-qc↗

arXiv2012

Modeling multipolar gravitational-wave emission from small mass-ratio mergers

Using the effective-one-body (EOB) formalism and a time-domain Teukolsky code, we generate inspiral, merger, and ringdown waveforms in the small mass-ratio limit. We use EOB inspiral and plunge trajectories to build the Teukolsky equation source term, and compute full coalescence waveforms for a range of black hole spins. By comparing EOB waveforms that were recently developed for comparable mass binary black holes to these Teukolsky waveforms, we improve the EOB model for the (2,2), (2,1), (3,3), and (4,4) modes. Our results can be used to quickly and accurately extract useful information about merger waves for binaries with spin, and should be useful for improving analytic models of such binaries.

gr-qc↗

arXiv2012

Numerical Techniques in Loop Quantum Cosmology

In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint equations to solve - generically, these are difference (rather than differential) equations. Important issues such as differing quantization methods, stability of the solutions, the semi-classical limit, and the relevance of lattice refinement in the difference equations are discussed. Finally, the cosmological models already considered in the literature are listed, along with typical features in these models and open issues.

gr-qc↗

arXiv2011

Null infinity waveforms from extreme-mass-ratio inspirals in Kerr spacetime

We describe the hyperboloidal compactification for Teukolsky equations in Kerr spacetime. We include null infinity on the numerical grid by attaching a hyperboloidal layer to a compact domain surrounding the rotating black hole and the orbit of an inspiralling point particle. This technique allows us to study, for the first time, gravitational waveforms from large- and extreme-mass-ratio inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons of our results with previous calculations establish the accuracy and efficiency of the hyperboloidal layer method.

gr-qc↗

arXiv2011

Testing the Cosmic Censorship Conjecture with point particles: the effect of radiation reaction and the self-force

A classical thought-experiment to destroy black holes was envisaged by Wald in 1974: it consists of throwing particles with large angular momentum into an extremal black hole, checking whether their capture can over-spin the black hole past the extremal limit and create a naked singularity. Wald showed that in the test-particle limit, particles that would be otherwise capable of producing naked singularities are simply scattered. Recently Jacobson and Sotiriou showed that if one considers instead a black hole that is almost, but not exactly extremal, then in the absence of backreaction effects particle capture could indeed over-spin the spacetime above the Kerr limit. Here we analyze back-reaction effects and show that for some of the trajectories giving rise to naked singularities, radiative effects can be neglected. However, for these orbits the conservative self-force is important, and seems to have the right sign to prevent the formation of naked singularities.

gr-qc↗

arXiv2011

Numerical modeling of gravitational wave sources accelerated by OpenCL

In this work, we make use of the OpenCL framework to accelerate an EMRI modeling application using the hardware accelerators -- Cell BE and Tesla CUDA GPU. We describe these compute technologies and our parallelization approach in detail, present our performance results, and then compare them with those from our previous implementations based on the native CUDA and Cell SDKs. The OpenCL framework allows us to execute identical source-code on both architectures and yet obtain strong performance gains that are comparable to what can be derived from the native SDKs.

gr-qc↗

arXiv2011

An Exploration of OpenCL for a Numerical Relativity Application

Currently there is considerable interest in making use of many-core processor architectures, such as Nvidia and AMD graphics processing units (GPUs) for scientific computing. In this work we explore the use of the Open Computing Language (OpenCL) for a typical Numerical Relativity application: a time-domain Teukolsky equation solver (a linear, hyperbolic, partial differential equation solver using finite-differencing). OpenCL is the only vendor-agnostic and multi-platform parallel computing framework that has been adopted by all major processor vendors. Therefore, it allows us to write portable source-code and run it on a wide variety of compute hardware and perform meaningful comparisons. The outcome of our experimentation suggests that it is relatively straightforward to obtain order-of-magnitude gains in overall application performance by making use of many-core GPUs over multi-core CPUs and this fact is largely independent of the specific hardware architecture and vendor. We also observe that a single high-end GPU can match the performance of a small-sized, message-passing based CPU cluster.

gr-qc↗

arXiv2011

Gravitational Wave Emission from the Single-Degenerate Channel of Type Ia Supernovae

The thermonuclear explosion of a C/O white dwarf as a Type Ia supernova (SN Ia) generates a kinetic energy comparable to that released by a massive star during a SN II event. Current observations and theoretical models have established that SNe Ia are asymmetric, and therefore--like SNe II--potential sources of gravitational wave (GW) radiation. We perform the first detailed calculations of the GW emission for a SN Ia of any type within the single-degenerate channel. The gravitationally-confined detonation (GCD) mechanism predicts a strongly-polarized GW burst in the frequency band around 1 Hz. Third-generation spaceborne GW observatories currently in planning may be able to detect this predicted signal from SNe Ia at distances up to 1 Mpc. If observable, GWs may offer a direct probe into the first few seconds of the SNe Ia detonation.

astro-ph.HE↗

arXiv2011

A multi-domain hybrid method for head-on collision of black holes in particle limit

A hybrid method is developed based on the spectral and finite-difference methods for solving the inhomogeneous Zerilli equation in time-domain. The developed hybrid method decomposes the domain into the spectral and finite-difference domains. The singular source term is located in the spectral domain while the solution in the region without the singular term is approximated by the higher-order finite-difference method. The spectral domain is also split into multi-domains and the finite-difference domain is placed as the boundary domain. Due to the global nature of the spectral method, a multi-domain method composed of the spectral domains only does not yield the proper power-law decay unless the range of the computational domain is large. The finite-difference domain helps reduce boundary effects due to the truncation of the computational domain. The multi-domain approach with the finite-difference boundary domain method reduces the computational costs significantly and also yields the proper power-law decay. Stable and accurate interface conditions between the finite-difference and spectral domains and the spectral and spectral domains are derived. For the singular source term, we use both the Gaussian model with various values of full width at half maximum and a localized discrete $δ$-function. The discrete $δ$-function was generalized to adopt the Gauss-Lobatto collocation points of the spectral domain. The gravitational waveforms are measured. Numerical results show that the developed hybrid method accurately yields the quasi-normal modes and the power-law decay profile. The numerical results also show that the power-law decay profile is less sensitive to the shape of the regularized $δ$-function for the Gaussian model than expected. The Gaussian model also yields better results than the localized discrete $δ$-function.

physics.comp-ph↗

arXiv2011

Systematics of black hole binary inspiral kicks and the slowness approximation

During the inspiral and merger of black holes, the interaction of gravitational wave multipoles carries linear momentum away, thereby providing an astrophysically important recoil, or "kick" to the system and to the final black hole remnant. It has been found that linear momentum during the last stage (quasinormal ringing) of the collapse tends to provide an "antikick" that in some cases cancels almost all the kick from the earlier (quasicircular inspiral) emission. We show here that this cancellation is not due to peculiarities of gravitational waves, black holes, or interacting multipoles, but simply to the fact that the rotating flux of momentum changes its intensity slowly. We show furthermore that an understanding of the systematics of the emission allows good estimates of the net kick for numerical simulations started at fairly late times, and is useful for understanding qualitatively what kinds of systems provide large and small net kicks.

gr-qc↗

arXiv2010

Test bodies and naked singularities: is the self-force the cosmic censor?

Jacobson and Sotiriou showed that rotating black holes could be spun-up past the extremal limit by the capture of non-spinning test bodies, if one neglects radiative and self-force effects. This would represent a violation of the Cosmic Censorship Conjecture in four-dimensional, asymptotically flat spacetimes. We show that for some of the trajectories giving rise to naked singularities, radiative effects can be neglected. However, for these orbits the conservative self-force is important, and seems to have the right sign to prevent the formation of naked singularities.

gr-qc↗

arXiv2010

Late-time Kerr tails: generic and non-generic initial data sets, "up" modes, and superposition

Three interrelated questions concerning Kerr spacetime late-time scalar-field tails are considered numerically, specifically the evolutions of generic and non-generic initial data sets, the excitation of "up" modes, and the resolution of an apparent paradox related to the superposition principle. We propose to generalize the Barack-Ori formula for the decay rate of any tail multipole given a generic initial data set, to the contribution of any initial multipole mode. Our proposal leads to a much simpler expression for the late-time power law index. Specifically, we propose that the late-time decay rate of the $Y_{\ell m}$ spherical harmonic multipole moment because of an initial $Y_{\ell' m}$ multipole is independent of the azimuthal number $m$, and is given by $t^{-n}$, where $n=\ell'+\ell+1$ for $\ell<\ell'$ and $n=\ell'+\ell+3$ for $\ell\ge\ell'$. We also show explicitly that the angular symmetry group of a multipole does not determine its late-time decay rate.

gr-qc↗

arXiv2010

High-Precision Numerical Simulations of Rotating Black Holes Accelerated by CUDA

Hardware accelerators (such as Nvidia's CUDA GPUs) have tremendous promise for computational science, because they can deliver large gains in performance at relatively low cost. In this work, we focus on the use of Nvidia's Tesla GPU for high-precision (double, quadruple and octal precision) numerical simulations in the area of black hole physics -- more specifically, solving a partial-differential-equation using finite-differencing. We describe our approach in detail and present the final performance results as compared with a single-core desktop processor and also the Cell BE. We obtain mixed results -- order-of-magnitude gains in overall performance in some cases and negligible gains in others.

physics.comp-ph↗

arXiv2010

Binary black hole merger gravitational waves and recoil in the large mass ratio limit

Spectacular breakthroughs in numerical relativity now make it possible to compute spacetime dynamics in almost complete generality, allowing us to model the coalescence and merger of binary black holes with essentially no approximations. The primary limitation of these calculations is now computational. In particular, it is difficult to model systems with large mass ratio and large spins, since one must accurately resolve the multiple lengthscales which play a role in such systems. Perturbation theory can play an important role in extending the reach of computational modeling for binary systems. In this paper, we present first results of a code which allows us to model the gravitational waves generated by the inspiral, merger, and ringdown of a binary system in which one member of the binary is much more massive than the other. This allows us to accurately calibrate binary dynamics in the large mass ratio regime. We focus in this analysis on the recoil imparted to the merged remnant by these waves. We closely examine the "antikick", an anti-phase cancellation of the recoil arising from the plunge and ringdown waves, described in detail by Schnittman et al. We find that, for orbits aligned with the black hole spin, the antikick grows as a function of spin. The total recoil is smallest for prograde coalescence into a rapidly rotating black hole, and largest for retrograde coalescence. Amusingly, this completely reverses the predicted trend for kick versus spin from analyses that only include inspiral information.

gr-qc↗

arXiv2009

The CBE Hardware Accelerator for Numerical Relativity: A Simple Approach

Hardware accelerators (such as the Cell Broadband Engine) have recently received a significant amount of attention from the computational science community because they can provide significant gains in the overall performance of many numerical simulations at a low cost. However, such accelerators usually employ a rather unfamiliar and specialized programming model that often requires advanced knowledge of their hardware design. In this article, we demonstrate an alternate and simpler approach towards managing the main complexities in the programming of the Cell processor, called software caching. We apply this technique to a numerical relativity application: a time-domain, finite-difference Kerr black hole perturbation evolver, and present the performance results. We obtain gains in the overall performance of generic simulations that are close to the theoretical maximum that can be obtained through our parallelization approach.

gr-qc↗

arXiv2009

An exploration of CUDA and CBEA for a gravitational wave source-modelling application

In this paper, we accelerate a gravitational physics numerical modelling application using hardware accelerators -- Cell processor and Tesla CUDA GPU. We describe these new technologies and our approach in detail, and then present our final performance results. We obtain well over an order-of-magnitude performance gain in our application by making use of these many-core architectures.

gr-qc↗

arXiv2009

A spectral collocation approximation for the radial-infall of a compact object into a Schwarzschild black hole

The inhomogeneous Zerilli equation is solved in time-domain numerically with the Chebyshev spectral collocation method to investigate a radial-infall of the point particle towards a Schwarzschild black hole. Singular source terms due to the point particle appear in the equation in the form of the Dirac $δ$-function and its derivative. For the approximation of singular source terms, we use the direct derivative projection method without any regularization. The gravitational waveforms are evaluated as a function of time. We compare the results of the spectral collocation method with those of the explicit second-order central-difference method. The numerical results show that the spectral collocation approximation with the direct projection method is accurate and converges rapidly when compared with the finite-difference method.

physics.comp-ph↗