Ruppeiner curvature along a renormalization group flow

TL;DR

This paper explores the Ruppeiner curvature of hyperbolic black holes in anti-de Sitter space and its relation to RG flows in dual conformal field theories, revealing universal and topology-dependent features.

Contribution

It demonstrates the behavior of Ruppeiner curvature along RG flows for hyperbolic black holes and identifies universal constants and topology effects.

Findings

Ruppeiner curvature indicates microstructure interactions in black holes.

Curvature along zero mass curve is a universal constant.

Extremal black holes have positive Ruppeiner curvature regardless of topology.

Abstract

We report on an investigation of Ruppeiner curvature $R_U$ for $(d+1)$-dimensional hyperbolic black holes in anti-de Sitter spacetimes and its connection with Renormalization Group (RG) flows in the dual d-dimensional conformal field theories (CFTs) in Minkowski spacetimes. A repulsive type interaction among microstructures is found, which is weaker for positive mass black holes and grows stronger for negative mass black holes at low temperatures. In particular, we show that $R_U$ evaluated along a zero mass curve is a universal constant, depending only on the dimension of space-time. The extremal black holes are pointed out to have a positive Ruppeiner curvature irrespective of their horizon topology.