Dirty black holes: Symmetries at stationary non-static horizons

Details Dirty black holes: Symmetries at stationary non-static horizons Dirty black holes: Symmetries at stationary non-static horizons

2004-03-05

arxiv.org/abs/gr-qc/0403026v1

Phys.Rev. D70 (2004) 024009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages; plain LaTeX

Scientific paper

10.1103/PhysRevD.70.024009

We establish that the Einstein tensor takes on a highly symmetric form near the Killing horizon of any stationary but non-static (and non-extremal) black hole spacetime. [This follows up on a recent article by the current authors, gr-qc/0402069, which considered static black holes.] Specifically, at any such Killing horizon -- irrespective of the horizon geometry -- the Einstein tensor block-diagonalizes into ``transverse'' and ``parallel'' blocks, and its transverse components are proportional to the transverse metric. Our findings are supported by two independent procedures; one based on the regularity of the on-horizon geometry and another that directly utilizes the elegant nature of a bifurcate Killing horizon. It is then argued that geometrical symmetries will severely constrain the matter near any Killing horizon. We also speculate on how this may be relevant to certain calculations of the black hole entropy.

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