Novel relations in massive gravity at Hawking-Page transition

TL;DR

This paper investigates how the Ruppeiner curvature at the Hawking-Page transition varies in massive gravity theories, revealing parameter dependencies and universal behavior at critical points, with implications for black hole microstructure understanding.

Contribution

It demonstrates that Ruppeiner curvature's universality at the Hawking-Page transition is broken in massive gravity, and identifies conditions where it reverts to a universal constant.

Findings

Ruppeiner curvature at HP transition depends on graviton mass and topology.

At a critical graviton mass, the curvature approaches a universal negative constant.

Near the transition, black hole geometries resemble decoupled Rindler spacetimes.

Abstract

Sign and magnitude of Ruppeiner's curvature $R_N$ is an empirical indicator of the respective nature and strength of microstructures of a thermodynamic system. For d-dimensional Schwarzschild black holes in AdS, $R_N$ at the Hawking-Page (HP) transition point is a universal constant. In this article we study the nature of $R_N$ at HP transition in a massive gravity theory and show that its constancy is broken due to the dependence on graviton mass as well as horizon topology. Although, when the graviton mass reaches a critical value the HP transition is driven to zero temperature, and $R_N$ at this point again approaches a universal negative constant, independent of all parameters of the theory. The geometry of black holes in AdS close to the HP transition point is also studied via novel near horizon scaling limits, and reveals the emergence of fully decoupled Rindler spacetimes.