Gravity and the thermodynamics of horizons

Abstract

Spacetimes with horizons showa resemblance to thermodynamic systems and it is possible to associate the notions of temperature andentrop y with them. Several aspects of this connection are reviewedin a manner appropriate for broadread ership. The approach uses two essential principles: (a) the physical theories must be formulatedfor 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 usedtogether 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, standardresults of quantum fieldtheory in curvedspacetimes with horizons can be obtainedd irectly (Sections 3–7). 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 8). The review emphasises the thermodynamic aspects of horizons, which couldbe obtainedfrom general principles andis expectedto remain valid, independent of the microscopicdescription (‘statistical mechanics’) of horizons.