Novel dual relation and constant in Hawking-Page phase transitions

TL;DR

This paper uncovers a novel dual relation between black hole temperatures and a universal constant in Hawking-Page phase transitions, offering new insights into black hole microstructure interactions and phase behavior.

Contribution

It introduces a new exact dual relation and identifies a universal constant in Ruppeiner curvature at the phase transition, advancing understanding of black hole thermodynamics.

Findings

Discovered a dual relation between minimum black hole temperature and phase transition temperature.

Identified a universal constant in Ruppeiner scalar curvature at the transition point.

Proposed the universal constant as an interaction threshold for black hole microstructures.

Abstract

Universal relations and constants have important applications in understanding a physical theory. In this article, we explore this issue for Hawking-Page phase transitions in Schwarzschild anti-de Sitter black holes. We find a novel exact dual relation between the minimum temperature of the ($d$+1)-dimensional black hole and the Hawking-Page phase transition temperature in $d$ dimensions, reminiscent of the holographic principle. Furthermore, we find that the normalized Ruppeiner scalar curvature is a universal constant at the Hawking-Page transition point. Since the Ruppeiner curvature can be treated as an indicator of the intensity of the interactions amongst black hole microstructures, we conjecture that this universal constant denotes an interaction threshold, beyond which a virtual black hole becomes a real one. This new dual relation and universal constant are fundamental in understanding Hawking-Page phase transitions, and might have new important applications in the black hole physics in the near future.