Entropy of three-dimensional asymptotically flat cosmological solutions

TL;DR

This paper explores the thermodynamics of three-dimensional asymptotically flat cosmological solutions, revealing their relation to black hole horizons and holographic principles, and highlighting the universality of the Massieu function.

Contribution

It demonstrates the thermodynamic properties of flat space cosmological solutions and connects them to black hole thermodynamics through holographic and semi-classical approaches.

Findings

Thermodynamics of flat space cosmological solutions matches the flat limit of black hole horizon thermodynamics.

The entropy relates to the semi-classical gravitational partition function.

The Massieu function is universal across different horizons.

Abstract

The thermodynamics of three-dimensional asymptotically flat cosmological solutions that play the same role than the BTZ black holes in the anti-de Sitter case is derived and explained from holographic properties of flat space. It is shown to coincide with the flat-space limit of the thermodynamics of the inner black hole horizon on the one hand and the semi-classical approximation to the gravitational partition function associated to the entropy of the outer horizon on the other. This leads to the insight that it is the Massieu function that is universal in the sense that it can be computed at either horizon.