Maximally Symmetric Spacetimes emerging from thermodynamic fluctuations

TL;DR

This paper demonstrates that maximally symmetric spacetimes like Minkowski, de Sitter, and Anti-de Sitter naturally emerge from the geometric structure of thermodynamic fluctuations, linking gravity and thermodynamics.

Contribution

It shows that these spacetimes can be derived from thermodynamic fluctuation theory, providing a novel connection between thermodynamics and vacuum solutions in gravity.

Findings

Maximally symmetric spacetimes are solutions to Einstein-Gauss-Bonnet theory from thermodynamic geometry.

Thermodynamic fluctuations correspond to Minkowski, de Sitter, and Anti-de Sitter spacetimes.

These solutions may be the only ones derivable from thermodynamic principles without additional assumptions.

Abstract

In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that the pseudo-Riemannian structure of the Thermodynamic Phase Space is a solution to the vacuum Einstein-Gauss-Bonnet theory of gravity with a cosmological constant. Then, we use the geometry of equilibrium thermodynamics to demonstrate that the maximally symmetric vacuum solutions of Einstein's Field Equations -- Minkowski, de-Sitter and Anti-de-Sitter spacetimes -- correspond to thermodynamic fluctuations. Moreover, we argue that these might be the only possible solutions that can be derived in this manner. Thus, the results presented here are the first concrete examples of spacetimes effectively emerging from the thermodynamic limit over an unspecified microscopic theory without any further assumptions.