We propose a simple definition of volume for stationary spacetimes. The proposed volume is constant in time, independent of the choice of stationary time slicing, and applies even in the absence of a globally timelike Killing vector. We then consider whether it is possible to construct spacetimes that have finite horizon area but infinite volume, by letting the radius go 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. This may constrain the statistical interpretation of the Bekenstein-Hawking entropy.
|Original language||English (US)|
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - 2006|
ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)