The role of gravitation in thermal physics (and thermo field theory)

Abstract

With his introduction of quantum mechanical considerations in the treatment of gravitating systems, Hawking indicated a way for the inclusion of general relativity into quantum (and, in particular, thermal) physics. However, probably the single most difficult phenomenon to deal with, subsequent to his work, has been the gravitational attraction of the very feature which his work leads to, viz, the thermal bath surrounding a black hole in equilibrium. It was not until York introduced a finite containing box for the system that certain problematical infinities could be removed and the treatment became well defined, with a sensible, describable, thermodynamic limit, and the possibility of finally realizing a satisfactory canonical ensemble for a black hole in a box. Gravitating systems could then be described thermodynamically, and the problem naturally admitted a path integral formulation which has been used to determine the contribution of non-classical geometries to the partition function for the black hole topological sector of the gravitational field. The application of this method to more familiar problems with a fixed space-time suggests an explicit interpretation of the theory of thermo field dynamics when thermal disturbances of the gravitational field can be ignored. This particular understanding may be extended to include small perturbative fluctuations of the geometry (loosely called gravitons) but it seems inappropriate for dealing with the actual structure of the space-time manifold, whereas gravitational thermodynamics, as referred to above, would remain perfectly adequate.