Gravity and the thermodynamics of horizons

Abstract

Abstract Spacetimes with horizons show a resemblance to thermodynamic systems and it is possible to associate the notions of temperature and entropy with them. Several as- pects of this connection are reviewed in a manner appropriate for broad readership. The approach uses two essential principles: (a) the physical theories must be formu- lated for each observer entirely in terms of variables any given observer can access and (b) consistent formulation of quantum field theory requires analytic continua- tion to the complex plane. These two principles, when used together in spacetimes with horizons, are powerful enough to provide several results in a unified manner. Since spacetimes with horizons have a generic behaviour under analytic continua- tion, standard results of quantum field theory in curved spacetimes with horizons can be obtained directly (Sections III to VII). The requirements (a) and (b) also put strong constraints on the action principle describing the gravity and, in fact, one can obtain the Einstein-Hilbert action from the thermodynamic considerations (Section VIII). The review emphasises the thermodynamic aspects of horizons, which could be obtained from general principles and is expected to remain valid, independent of the microscopic description (‘statistical mechanics’) of horizons.