Entropy of three-dimensional asymptotically flat cosmological solutions

TL;DR

This work derives the thermodynamics of three-dimensional asymptotically flat cosmological solutions and presents a holographic framing via flat-space holography anchored in the ${\rm BMS}_3$ algebra. It shows that the cosmological horizon thermodynamics coincide with the flat-space limit of the inner BTZ horizon and that the semi-classical partition function around the outer horizon yields a Massieu function universal to both horizons. A Cardy-like formula for the flat-space partition function is established, with high-temperature behavior giving $\ln Z_{Cardy} = \frac{π^2}{2G β μ_E^2}$, matching the flat-space thermodynamics. The results emphasize a universal Massieu function, robust under the flat-space limit and horizon interchange, and they illuminate how AdS3 results contract to flat space in a holographic context. These findings bolster flat-space holography in 3D and suggest avenues for extending the universality of horizon thermodynamics to other spacetimes and dimensions.

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.