Hyperboloidal evolution of test fields in three spatial dimensions

Zenginoğlu, Anıl; Kidder, Lawrence E.

doi:10.1103/physrevd.81.124010

Cited by 21 publications

(37 citation statements)

References 51 publications

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“…The application of the method in black-hole spacetimes proved to be difficult [76][77][78][79][80], until the general construction of suitable hyperboloidal scri-fixing coordinates on asymptotically flat spacetimes has been presented [81]. Since then, hyperboloidal scri-fixing coordinates have been employed in a rich variety of problems concerning black-hole spacetimes [22,[82][83][84][85][86][87][88][89][90][91].…”

Section: Introductionmentioning

confidence: 99%

Binary black hole coalescence in the large-mass-ratio limit: The hyperboloidal layer method and waveforms at null infinity

Bernuzzi¹,

2011

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We compute and analyze the gravitational waveform emitted to future null infinity by a system of two black holes in the large-mass-ratio limit. We consider the transition from the quasiadiabatic inspiral to plunge, merger, and ringdown. The relative dynamics is driven by a leading order in the mass ratio, 5PN-resummed, effective-one-body (EOB), analytic-radiation reaction. To compute the waveforms, we solve the Regge-Wheeler-Zerilli equations in the time-domain on a spacelike foliation, which coincides with the standard Schwarzschild foliation in the region including the motion of the small black hole, and is globally hyperboloidal, allowing us to include future null infinity in the computational domain by compactification. This method is called the hyperboloidal layer method, and is discussed here for the first time in a study of the gravitational radiation emitted by black hole binaries. We consider binaries characterized by five mass ratios, ¼ 10 À2;À3;À4;À5;À6 , that are primary targets of space-based or thirdgeneration gravitational wave detectors. We show significative phase differences between finite-radius and null-infinity waveforms. We test, in our context, the reliability of the extrapolation procedure routinely applied to numerical relativity waveforms. We present an updated calculation of the final and maximum gravitational recoil imparted to the merger remnant by the gravitational wave emission, v end kick =ðc 2 Þ ¼ 0:04474 AE 0:00007 and v max kick =ðc 2 Þ ¼ 0:05248 AE 0:00008. As a self-consistency test of the method, we show an excellent fractional agreement (even during the plunge) between the 5PN EOB-resummed mechanical angular momentum loss and the gravitational wave angular momentum flux computed at null infinity. New results concerning the radiation emitted from unstable circular orbits are also presented. The high accuracy waveforms computed here could be considered for the construction of template banks or for calibrating analytic models such as the effective-one-body model.

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Section: Introductionmentioning

confidence: 99%

Binary black hole coalescence in the large-mass-ratio limit: The hyperboloidal layer method and waveforms at null infinity

Bernuzzi¹,

2011

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“…For schemes compactifying spacelike infinity; see [335, 336]. Conformal compactifications are reviewed in [172, 183], and a partial list of references to date includes [328, 176, 177, 180, 179, 170, 245, 172, 247, 100, 446, 447, 316, 87, 451, 452, 448, 449, 450, 305, 364, 42]. …”

Section: Boundary Conditions For Einstein’s Equationsmentioning

confidence: 99%

“…In numerical relativity, the projection method for outer boundary conditions has been used in references [102, 103, 421, 278, 225], the penalty FD one for multi-domain boundary conditions in [281, 141, 385, 145, 324, 325, 425, 256, 454, 426], and for spectral methods in — among many others — [130, 289, 90, 168, 306, 450, 402, 131, 149, 290, 97, 91, 31, 381, 150, 384]. …”

Section: Numerical Boundary Conditionsmentioning

confidence: 99%

Continuum and Discrete Initial-Boundary Value Problems and Einstein’s Field Equations

Sarbach

Tiglio

2012

Living Rev. Relativ.

150

168

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Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black-hole problem within Einstein’s theory of gravitation, in which one computes the gravitational radiation emitted from the inspiral of the two black holes, merger and ringdown. Powerful mathematical tools can be used to establish qualitative statements about the solutions, such as their existence, uniqueness, continuous dependence on the initial data, or their asymptotic behavior over large time scales. However, one is often interested in computing the solution itself, and unless the partial differential equation is very simple, or the initial data possesses a high degree of symmetry, this computation requires approximation by numerical discretization. When solving such discrete problems on a machine, one is faced with a finite limit to computational resources, which leads to the replacement of the infinite continuum domain with a finite computer grid. This, in turn, leads to a discrete initial-boundary value problem. The hope is to recover, with high accuracy, the exact solution in the limit where the grid spacing converges to zero with the boundary being pushed to infinity.The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein’s equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.

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“…The only numerical computations of black-hole perturbations using the hyperboloidal method without spherical symmetry deal with scalar perturbations [62][63][64][65]. One goal of this paper is to present the application of the hyperboloidal method to Teukolsky equations in Kerr spacetime for the calculation of gravitational waveforms at null infinity.…”

Section: Introductionmentioning

confidence: 99%

Null Infinity Waveforms from Extreme-Mass-Ratio Inspirals in Kerr Spacetime

Zenginoğlu

Khanna

2011

Phys. Rev. X

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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.

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Hyperboloidal evolution of test fields in three spatial dimensions

Cited by 21 publications

References 51 publications

Binary black hole coalescence in the large-mass-ratio limit: The hyperboloidal layer method and waveforms at null infinity

Binary black hole coalescence in the large-mass-ratio limit: The hyperboloidal layer method and waveforms at null infinity

Continuum and Discrete Initial-Boundary Value Problems and Einstein’s Field Equations

Null Infinity Waveforms from Extreme-Mass-Ratio Inspirals in Kerr Spacetime

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