Thermodynamics in space-times without horizons

TL;DR

This paper explores the thermodynamics of horizonless spacetimes with a preferred timelike surface, revealing unique energetic and thermodynamic properties, including zero energy surfaces and area-proportional entropy.

Contribution

It introduces a framework for analyzing the thermodynamics of horizonless spacetimes with a preferred surface, extending black hole thermodynamics concepts to new geometries.

Findings

Surfaces can have zero energy, simplifying the spacetime energetics.

Entropy is proportional to the area of the timelike surface.

The matter temperature relates to surface gravity and transverse pressure.

Abstract

We consider the energetics and thermodynamics of spacetimes with no horizons, but endowed with a preferred timelike junction surface. They could arise as a limiting case of the gravastar and other constructions regularizing the interior of the horizon of a black hole, or from the conceptual cutting of a portion of a non-asymptotically flat space and gluing it with flat space. We find that such surfaces can be made to have zero energy, so that the energetics of such spaces is not encumbered by them. They do have a transverse pressure, fixed by the jump in surface gravity. A peculiar matter thermodynamics then follows, with well defined entropy, temperature and surface pressure, constrained by specific relations arising from the zero energy condition. This is confirmed by the Euclidean path integral, with the proviso that the Tolman-Ehrenfest temperature should be used. The entropy of the space is then the area of the timelike surface in units of a fundamental area, and the matter temperature is proportional to the transverse pressure and so the jump in surface gravity. However, when the gravitational action is added, the free energy of the surface is also zero. The fact that for some such spaces the temperature comes out negative raises interesting questions regarding the third law of thermodynamics.