Symmetries at stationary Killing horizons

Details Symmetries at stationary Killing horizons Symmetries at stationary Killing horizons

2004-10-21

arxiv.org/abs/gr-qc/0410103v1

Gen.Rel.Grav. 37 (2005) 1947-1956

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, Revtex

Scientific paper

10.1007/s10714-005-0172-2

It has often been suggested (especially by Carlip) that spacetime symmetries in the neighborhood of a black hole horizon may be relevant to a statistical understanding of the Bekenstein-Hawking entropy. A prime candidate for this type of symmetry is that which is exhibited by the Einstein tensor. More precisely, it is now known that this tensor takes on a strongly constrained (block-diagonal) form as it approaches any stationary, non-extremal Killing horizon. Presently, exploiting the geometrical properties of such horizons, we provide a particularly elegant argument that substantiates this highly symmetric form for the Einstein tensor. It is, however, duly noted that, on account of a "loophole", the argument does fall just short of attaining the status of a rigorous proof.

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