Black holes and partition functions.
Abstract
The train of developments leading from the early viewpoint on black hole thermodynamics to the present understanding in terms of statistical thermodynamics of the gravitational field in black hole topologies is reviewed. The key idea is to take into strict account the boundary conditions, that is, the information supposed to be known to a given observer, in constructing appropriate ensembles. Statistical mechanics of gravitational fields describing the black hole topological sector, and the correspondence to thermodynamics, are then discussed in the canonical ensemble. The Euclidean action is evaluated on the constraint hypersurface and a measure is obtained from a heuristic argument, resulting in a path-integral form of the canonical partition function. From this one obtains the usual black-hole entropy, supplemented by statistical corrections when the temperature and size of the system are appropriate. Under other boundary conditions, it follows that a phase transition (change of topology) must occur.
- Publication:
-
Conceptual Problems of Quantum Gravity
- Pub Date:
- 1991
- Bibcode:
- 1991cpqg.conf..573Y