Local Temperature in Curved Spacetime

TL;DR

This paper introduces a local temperature concept in quantum field theory on curved spacetime, demonstrating that equilibrium states can have varying local temperatures and challenging the idea of a global temperature in such settings.

Contribution

It presents a new local temperature definition in curved spacetime and applies it to de Sitter space, highlighting limitations of global temperature notions.

Findings

Equilibrium states exhibit non-uniform local temperatures near horizons.

Global temperature concepts may not be consistent in curved spacetime.

Local temperature varies in the neighborhood of a geodesic observer.

Abstract

A physically meaningful local concept of temperature is introduced in quantum field theory on curved spacetime and applied to the example of a massless field on de Sitter space. It turns out in this model that the equilibrium (Gibbs) states which can be prepared by a geodesic observer have in general a varying temperature distribution in the neighborhood of the geodesic and may not even allow for a consistent thermal interpretation close to the horizon. This result, which can be traced back to the Unruh effect, illustrates the failure of a global notion of temperature in curved spacetime and reveals the need for a local concept, as presented here.