Global equilibrium and local thermodynamics in stationary spacetimes

TL;DR

This paper explores how global equilibrium states in stationary spacetimes can be characterized using local thermodynamic fields derived from geometry, illustrated through a scalar field in Einstein's static universe.

Contribution

It introduces a framework for defining equilibrium states via local thermodynamics based solely on geometric properties of stationary spacetimes.

Findings

Equilibrium states can have inhomogeneous thermodynamic properties.

Such states can possess nonvanishing angular momentum.

The approach applies to scalar fields in Einstein's static universe.

Abstract

In stationary spacetimes global equilibrium states can be defined, applying the maximum entropy principle, by the introduction of local thermodynamic fields determined solely by geometry. As an example, we study a class of equilibrium states for a scalar field in Einstein's static universe, characterized by inhomogeneous thermodynamic properties and nonvanishing angular momentum.