Critical phenomena and information geometry in black hole physics

TL;DR

This paper explores how information geometry, specifically Ruppeiner geometry, can analyze stability and critical phenomena in black hole physics, providing insights into black hole thermodynamics and extremality.

Contribution

It applies thermodynamic geometry to black holes, demonstrating its effectiveness in analyzing stability, critical points, and physical properties like specific heat and extremality.

Findings

Ruppeiner geometry aligns with Poincare stability analysis.

Sign of specific heat and extremality are encoded in the metric.

Applicable to Myers-Perry black holes.

Abstract

We discuss the use of information geometry in black hole physics and present the outcomes. The type of information geometry we utilize in this approach is the thermodynamic (Ruppeiner) geometry defined on the state space of a given thermodynamic system in equilibrium. The Ruppeiner geometry can be used to analyze stability and critical phenomena in black hole physics with results consistent with those from the Poincare stability analysis for black holes and black rings. Furthermore other physical phenomena are well encoded in the Ruppeiner metric such as the sign of specific heat and the extremality of the solutions. The black hole families we discuss in particular in this manuscript are the Myers-Perry black holes.