Gravity and the Thermodynamics of Horizons

TL;DR

This paper reviews how spacetimes with horizons exhibit thermodynamic properties like temperature and entropy, and explores the deep connection between gravity, horizon thermodynamics, and quantum field theory.

Contribution

It demonstrates that the Einstein-Hilbert action can be derived from thermodynamic principles and emphasizes the role of observer-dependent variables and analytic continuation in understanding horizons.

Findings

Standard quantum field theory results in curved spacetime are derived from principles (a) and (b).

The Einstein-Hilbert action can be obtained from thermodynamic considerations.

Insights into the semiclassical limit of quantum gravity are provided.

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 aspects of this connection are reviewed in a manner appropriate for broad readership. The approach uses two essential principles: (a) the physical theories must be formulated for each observer entirely in terms of variables any given observer can access and (b) consistent formulation of quantum field theory requires analytic continuation 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 continuation, 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. The latter part of the review (Sections VIII to X) investigates this deeper connection between gravity, spacetime microstructure and thermodynamics of horizons. This approach leads to several interesting results in the semiclassical limit of quantum gravity, which are described.