Solving the Initial Value Problem of Two Black Holes

Marronetti, Pedro; Matzner, Richard A.

doi:10.1103/physrevlett.85.5500

Cited by 49 publications

(80 citation statements)

References 13 publications

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“…The reason for this is that, until very recently, most of the initial data typically used in numerical relativity were for maximal slicing, and thus reduced, in the various regimes where perturbation is used (far region, late times, initially close black holes, etc), precisely to the Schwarzschild and Kerr spacetimes in Schwarzschild and Boyer-Lindquist coordinates, respectively. In recent years, however, work was started on Kerr-Schild-type initial data [13], which are not maximal. Part of the motivation for introducing this new kind of initial data is to avoid the typical grid stretching that maximal slicings produce near the event horizon 1 , a stretching that eventually causes numerical simulations to crash 2 .…”

Section: Introductionmentioning

confidence: 99%

Gauge-invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates

2001

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We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing of a Schwarzschild black hole. We explain how to obtain the gauge-invariant part of the metric perturbations from the amplitudes obeying our generalized Regge-Wheeler and Zerilli equations and vice-versa. We also give a general expression for the radiated energy at infinity, and establish the relation between our geometrical equations and the Teukolsky formalism. The results presented in this paper are expected to be useful for the close-limit approximation to black hole collisions, for the Cauchy perturbative matching problem, and for the study of isolated horizons.

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Section: Introductionmentioning

confidence: 99%

Gauge-invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates

2001

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“…Several groups have been achieved to construct binary black hole initial data successfully [9,10,11,12,13,14,15,16,17,18], (for earlier works, see [19]). …”

Section: Introductionmentioning

confidence: 99%

“…(11) in a region between two concentric spheres S a and S b with radius r = r a and r = r b (r a < r b ) where Dirichlet conditions are imposed. Its radial part g DD ℓ (r, r ′ ) associated with the ℓth mode is written…”

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confidence: 99%

Numerical method for binary black hole/neutron star initial data: Code test

Tsokaros

Uryū

2007

Phys. Rev. D

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A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; Two of these are centered at the binary compact objects and cover a neighborhood of each object; the third patch extends to the asymptotic region. As in the Komatsu-Eriguchi-Hachisu method, nonlinear elliptic field equations are decomposed into a flat space Laplacian and a remaining nonlinear expression that serves in each iteration as an effective source. The equations are solved iteratively, integrating a Green's function against the effective source at each iteration. Detailed convergence tests for the essential part of the code are performed for a few types of selected Green's functions to treat different boundary conditions. Numerical computation of the gravitational potential of a fluid source, and a toy model for a binary black hole field are carefully calibrated with the analytic solutions to examine accuracy and convergence of the new code. As an example of the application of the code, an initial data set for binary black holes in the Isenberg-Wilson-Mathews formulation is presented, in which the apparent horizons are located using a method described in Appendix A.

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“…There have been numerous efforts to find astrophysically accurate initial data for binary systems [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27], which usually consist of the 3-metric and extrinsic curvature. Most methods rely on performing decompositions of the data to separate the so called physical degrees of freedom from those constrained by the Einstein equations and those associated with diffeomorphisms.…”

Section: Introductionmentioning

confidence: 99%

Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions

Yunes

Tichy

2006

Phys. Rev. D

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We construct approximate initial data for non-spinning black hole binary systems by asymptotically matching the 4-metrics of two tidally perturbed Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian 4-metric in ADMTT coordinates. The specific matching procedure used here closely follows the calculation in [1], and is performed in the so called buffer zone where both the post-Newtonian and the perturbed Schwarzschild approximations hold. The result is that both metrics agree in the buffer zone, up to the errors in the approximations. However, since isotropic coordinates are very similar to ADMTT coordinates, matching yields better results than in the previous calculation [1], where harmonic coordinates were used for the post-Newtonian 4-metric. In particular, not only does matching improve in the buffer zone, but due to the similarity between ADMTT and isotropic coordinates the two metrics are also close to each other near the black hole horizons. With the help of a transition function we also obtain a global smooth 4-metric which has errors on the order of the error introduced by the more accurate of the two approximations we match. This global smoothed out 4-metric is obtained in ADMTT coordinates which are not horizon penetrating. In addition, we construct a further coordinate transformation that takes the 4-metric from global ADMTT coordinates to new coordinates which are similar to Kerr-Schild coordinates near each black hole, but which remain ADMTT further away from the black holes. These new coordinates are horizon penetrating and lead, for example, to a lapse which is everywhere positive on the t = 0 slice. Such coordinates may be more useful in numerical simulations.

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Solving the Initial Value Problem of Two Black Holes

Cited by 49 publications

References 13 publications

Gauge-invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates

Gauge-invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates

Numerical method for binary black hole/neutron star initial data: Code test

Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions

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