Dynamics of Apparent and Event Horizons

Anninos, Peter; Bernstein, David; Brandt, Steven R.; Libson, Joseph; Massó, Joan; Seidel, Edward; Smarr, Larry; Suen, Wai-Mo; Walker, Paul

doi:10.1103/physrevlett.74.630

Cited by 69 publications

(137 citation statements)

References 12 publications

(11 reference statements)

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“…We have to confront with this issue to resolve the information loss paradox. There have been many works concerning black hole evaporation, either in string theories [2][3] [4], or semiclassical theory typically using apparent horizon [5]. Hiscok studied spherical model of the black hole evaporation using the Vaidya metric, which we also use in present work, to solve the black hole evaporation problem.…”

Section: Introductionmentioning

confidence: 99%

Evaporating dynamical horizon with the Hawking effect in Vaidya spacetime

Sawayama

2006

Phys. Rev. D

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Section: Introductionmentioning

confidence: 99%

Evaporating dynamical horizon with the Hawking effect in Vaidya spacetime

Sawayama

2006

Phys. Rev. D

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“…In the case of asymmetric binary black hole coalescence it is conjectured that the level set Γ, which corresponds to a section of the event horizon, must take a higher genus topology at merger. To investigate this possibility, figure (14) shows the level setΓ viewed along the axis joining the centers of the apparent horizons. In that figure it is apparent that the throat function of the topological transition is elliptical in geometry.…”

Section: Change Of Topologymentioning

confidence: 99%

“…Consequently, the binary black hole coalescence problem has become an active subject of numerical relativity. One particular problem in the computational domain is the computational definition, detection and tracking of the black hole event horizon itself [13], [14], [15], [16], [17], [18].…”

Section: Introductionmentioning

confidence: 99%

Tracking black holes in numerical relativity

2003

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This work addresses and solves the problem of generically tracking black hole event horizons in computational simulation of black hole interactions. Solutions of the hyperbolic eikonal equation, solved on a curved spacetime manifold containing black hole sources, are employed in development of a robust tracking method capable of continuously monitoring arbitrary changes of topology in the event horizon, as well as arbitrary numbers of gravitational sources. The method makes use of continuous families of level set viscosity solutions of the eikonal equation with identification of the black hole event horizon obtained by the signature feature of discontinuity formation in the eikonal's solution. The method is employed in the analysis of the event horizon for the asymmetric merger in a binary black hole system. In this first such three dimensional analysis, we establish both qualitative and quantitative physics for the asymmetric collision; including: 1. Bounds on the topology of the throat connecting the holes following merger, 2. Time of merger, and 3. Continuous accounting for the surface of section areas of the black hole sources.

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“…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]. 3 Schnetter [41,42] has developed an apparent horizon finding algorithm and code quite similar to mine.…”

Section: Notationmentioning

confidence: 99%

“…In the limit of small xyz, a cubic Hermite geometry interpolator gives g ij and K ij to O(( xyz) 4 ) and 3 ) errors to . However, at practical resolutions of xyz ∼ 0.03m-0.1m I find that the convergence is often 0.5-1.0 power of xyz better than this, only dropping to the theoretical limits for very high-resolution grids (in practice, xyz 0.01m).…”

Section: Accuracymentioning

confidence: 99%

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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Dynamics of Apparent and Event Horizons

Cited by 69 publications

References 12 publications

Evaporating dynamical horizon with the Hawking effect in Vaidya spacetime

Evaporating dynamical horizon with the Hawking effect in Vaidya spacetime

Tracking black holes in numerical relativity

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

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