NSF-ITP-97-019 gr-qc/97mmnnn Black Hole Boundary Conditions and Coordinate Conditions
نویسنده
چکیده
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. Typeset using REVTEX ∗Electronic address: [email protected]
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