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General Relativity and Gravitation

, Volume 37, Issue 12, pp 1947–1956 | Cite as

Symmetries at stationary Killing horizons

  • A. J. M. Medved
Research Article

Abstract

It has often been suggested (especially by S. 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 one 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.

Keywords

Black hole Entropy 

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.School of Mathematics, Statistics and Computer ScienceVictoria University of WellingtonWellingtonNew Zealand

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