Evolution of time-symmetric gravitational waves: Initial data and apparent horizons

Eppley, K.

doi:10.1103/physrevd.16.1609

Cited by 62 publications

(126 citation statements)

References 6 publications

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“…on a 3-dimensional spacelike hypersurface) and are then stepped to the next instant using an "ADM" [2] form of the Einstein evolution equations [3]. The evolution is unconstrained, and maintenance of the constraint functions with small error is verified throughout the run.This work extends previous work on headon encounters [4][5][6][7]. It is comparable to recent results of Brügmann [8]: non-headon black hole evolution through to significant interaction and merger.…”

supporting

confidence: 80%

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Grazing Collisions of Black Holes via the Excision of Singularities

et al. 2000

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We present the first simulations of non-headon (grazing) collisions of binary black holes in which the black hole singularities have been excised from the computational domain. Initially two equal mass black holes m are separated a distance ≈ 10m and with impact parameter ≈ 2m. Initial data are based on superposed, boosted (velocity ≈ 0.5c) solutions of single black holes in Kerr-Schild coordinates. Both rotating and non-rotating black holes are considered. The excised regions containing the singularities are specified by following the dynamics of apparent horizons. Evolutions of up to t ≈ 35m are obtained in which two initially separate apparent horizons are present for t ≈ 3.8m. At that time a single enveloping apparent horizon forms, indicating that the holes have merged. Apparent horizon area estimates suggest gravitational radiation of about 2.6% of the total mass. The evolutions end after a moderate amount of time because of instabilities.Introduction: Gravitational wave detectors [1] will soon begin searching for gravitational radiation from astrophysical binary compact objects. To understand these observations, and to predict parameter regimes in which to search for their radiation, efforts are underway to model the interaction of compact sources. We report here a direct numerical simulation of interacting spinning black hole binaries, in genuinely hyperbolic (nonheadon) trajectories. The initial spin angular momenta evolved here are either zero, or parallel to each other and perpendicular to the orbital plane. The interior of the equal mass holes and their interior singularities are excised from the computation. (Our method is neither restricted to equal masses nor to parallel spins). Evolution is carried out in a Cauchy scheme, in which the state of the gravitational system (the 3-spatial metric g ab ) and its rate of change (the 3-spatial extrinsic curvature K ab ) are specified at one instant (i.e. on a 3-dimensional spacelike hypersurface) and are then stepped to the next instant using an "ADM" [2] form of the Einstein evolution equations [3]. The evolution is unconstrained, and maintenance of the constraint functions with small error is verified throughout the run.This work extends previous work on headon encounters [4][5][6][7]. It is comparable to recent results of Brügmann [8]: non-headon black hole evolution through to significant interaction and merger. But our approach has a novel feature: the singularity-excising character of the computation of generic encounters which allows "natural" motion of the black holes through the computational

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supporting

confidence: 80%

“…This work extends previous work on headon encounters [4][5][6][7]. It is comparable to recent results of Brügmann [8]: non-headon black hole evolution through to significant interaction and merger.…”

supporting

confidence: 80%

Grazing Collisions of Black Holes via the Excision of Singularities

et al. 2000

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“…In axisymmetry, the apparent horizon is located at a distance r C ; h from a point C located on the axis of symmetry, where h satisfies the following ordinary differential equation [43] …”

Section: The Apparent Horizonmentioning

confidence: 99%

Approximate initial data for binary black holes

2006

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We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the transverse-traceless decomposition and consider perturbations of Schwarzschild black holes caused by boosts and the presence of a binary companion. A superposition of these two perturbations then yields approximate, but fully analytic binary black hole initial data that are accurate to first order in the inverse of the binary separation and the square of the black holes' momenta.

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“…(For earlier numerical evidence see Eppley [17] and Miyama [18].) Our construction is based in an essential manner on the conformal approach (see Choquet-Bruhat and York [19]) to solving the constraints of General Relativity.…”

Section: Introductionmentioning

confidence: 99%

Trapped surfaces in vacuum spacetimes

Beig¹,

Murchadha²

1994

Class. Quantum Grav.

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An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric case considered previously, to the case of maximal slices. The resulting theorem shows rigorously that there exists a large class of initial configurations for non-time symmetric pure gravitational waves satisfying the assumptions of the Penrose singularity theorem and so must have a singularity to the future. *) Supported by Fonds zur Förderung der wissenschaftlichen Forschung inÖsterreich, Projekt Nr. P9376-PHY.

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Evolution of time-symmetric gravitational waves: Initial data and apparent horizons

Cited by 62 publications

References 6 publications

Grazing Collisions of Black Holes via the Excision of Singularities

Grazing Collisions of Black Holes via the Excision of Singularities

Approximate initial data for binary black holes

Trapped surfaces in vacuum spacetimes

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