Black Hole Boundary Conditions and Coordinate Conditions

Details Black Hole Boundary Conditions and Coordinate Conditions Black Hole Boundary Conditions and Coordinate Conditions

1997-03-11

arxiv.org/abs/gr-qc/9703027v2

Phys.Rev. D57 (1998) 2299-2304

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages LaTeX, revtex. No figures

Scientific paper

10.1103/PhysRevD.57.2299

This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further condition is necessary for the system to be well posed; the ``prescribed curvature conditions" are therefore proposed to complete the coordinate conditions at the black hole. These conditions lead to a system of two 2D elliptic differential equations on the inner boundary surface, which coexist nicely to the 3D equation for maximal slicing (or related slicing conditions). The overall 2D/3D system is argued to be well posed and globally well behaved. The importance of ``boundary conditions without boundary values" is emphasized. This paper is the first of a series. This revised version makes minor additions and corrections to the previous version.

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