The Volume of Black Holes

Details The Volume of Black Holes The Volume of Black Holes

2005-08-16

arxiv.org/abs/hep-th/0508108v1

Phys.Rev. D73 (2006) 124021

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, revtex

Scientific paper

10.1103/PhysRevD.73.124021

We propose a definition of volume for stationary spacetimes. The proposed volume is independent of the choice of stationary time-slicing, and applies even though the Killing vector may not be globally timelike. Moreover, it is constant in time, as well as simple: the volume of a spherical black hole in four dimensions turns out to be just ${4 \over 3} \pi r_+^3$. We then consider whether it is possible to construct spacetimes that have finite horizon area but infinite volume, by sending the radius to infinity while making discrete identifications to preserve the horizon area. We show that, in three or four dimensions, no such solutions exist that are not inconsistent in some way. We discuss the implications for the interpretation of the Bekenstein-Hawking entropy.

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