Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-02-15
Class.Quant.Grav. 21 (2004) 3111-3126
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages, plain LaTeX. V2: Discussion regarding extremal horizons corrected. Two references addded. No other physics changes
Scientific paper
10.1088/0264-9381/21/13/003
We consider the spacetime geometry of a static but otherwise generic black hole (that is, the horizon geometry and topology are not necessarily spherically symmetric). It is demonstrated, by purely geometrical techniques, that the curvature tensors, and the Einstein tensor in particular, exhibit a very high degree of symmetry as the horizon is approached. Consequently, the stress-energy tensor will be highly constrained near any static Killing horizon. More specifically, it is shown that -- at the horizon -- the stress-energy tensor block-diagonalizes into ``transverse'' and ``parallel'' blocks, the transverse components of this tensor are proportional to the transverse metric, and these properties remain invariant under static conformal deformations. Moreover, we speculate that this geometric symmetry underlies Carlip's notion of an asymptotic near-horizon conformal symmetry controlling the entropy of a black hole.
Martin Damien
Medved A. J. M.
Visser Matt
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