Test-beds and applications for apparent horizon finders in numerical relativity

Alcubierre, Miguel; Brandt, Steven R.; Brügmann, Bernd; Gundlach, Carsten; Massó, Joan; Seidel, Edward; Walker, Paul

doi:10.1088/0264-9381/17/11/301

Cited by 47 publications

(87 citation statements)

References 54 publications

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“…The mass is calculated from the decay of ψ in the asymptotic region. We also show the results of previous calculations by Holz et al [4] and Alcubierre et al [5], which are in excellent agreement. All our results were calculated on a 600 × 600 grid.…”

Section: Introductionsupporting

confidence: 89%

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Apparent horizons in simplicial Brill wave initial data

Gentle

Holz

Miller

et al. 1999

Class. Quantum Grav.

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Abstract. We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of initial data, and provide an independent verification of the existence of an apparent horizon once a critical gravitational wave amplitude is passed. Our estimate of this critical value, using both the Regge and continuum solutions, supports other recent findings.

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Section: Introductionsupporting

confidence: 89%

“…In particular, we study the formation of apparent horizons within the simplicial initial data, and confirm recent findings regarding the appearance of such horizons [5].…”

Section: Introductionsupporting

confidence: 87%

Apparent horizons in simplicial Brill wave initial data

Gentle

Holz

Miller

et al. 1999

Class. Quantum Grav.

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“…I did convergence tests [14] in both grid spacings to verify that the values shown are reliable estimates of the true continuum values, and I used Richardson extrapolation in the angular grid spacing to improve the accuracy 17 . Table 2 shows the results, together with values reported by [1] for comparison. The AHFINDERDIRECT values are in excellent agreement with those of [1], and are dramatically more accurate.…”

Section: Misner and Brill-lindquist Slicesmentioning

confidence: 99%

“…In cases where the distinction is important, I use a prefix (3) to denote quantities defined on a 3D (three-dimensional) neighbourhood of the apparent horizon surface. 1 For more recent work on this topic, see (for example) [2,3,11,15]. 2 For numerical purposes the usual approximate development to a nearly stationary state suffices [4,13,21,32].…”

Section: Notationmentioning

confidence: 99%

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A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity

Thornburg¹

2003

AIP Conference Proceedings

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In 3 + 1 numerical simulations of dynamic black-hole spacetimes, it is useful to be able to find the apparent horizon(s) (AH) in each slice of a time evolution. A number of AH finders are available, but they often take many minutes to run, so they are too slow to be practically usable at each time step. Here I present a new AH finder, AHFINDERDIRECT, which is very fast and accurate: at typical resolutions it takes only a few seconds to find an AH to ∼10 −5 m accuracy on a GHz-class processor. I assume that an AH to be searched for is a Strahlkörper ('star-shaped region') with respect to some local origin, and so parametrize the AH shape by r = h (angle) for some single-valued function h : S 2 → + . The AH equation then becomes a nonlinear elliptic PDE in h on S 2 , whose coefficients are algebraic functions of g ij , K ij , and the Cartesian-coordinate spatial derivatives of g ij . I discretize S 2 using six angular patches (one each in the neighbourhood of the ±x, ±y, and ±z axes) to avoid coordinate singularities, and finite difference the AH equation in the angular coordinates using fourth-order finite differencing. I solve the resulting system of nonlinear algebraic equations (for h at the angular grid points) by Newton's method, using a 'symbolic differentiation' technique to compute the Jacobian matrix. AHFINDERDIRECT is implemented as a thorn in the CACTUS computational toolkit, and is freely available by anonymous CVS checkout. * Appendix B on 'multiprocessor and parallelization issues' and appendix C on 'searching for the critical parameter of a 1-parameter initial data sequence' also appear in the preprint-archive version of this paper (gr-qc/0306056).

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