Information geometry of asymptotically AdS black holes

TL;DR

This paper explores the thermodynamic geometries of asymptotically AdS black holes, revealing nontrivial geometric structures in certain cases and analyzing the role of the cosmological constant as a parameter.

Contribution

It provides a comparative analysis of thermodynamic geometries of Reissner-Nordström AdS and BTZ black holes, highlighting the effects of the AdS background and cosmological constant.

Findings

AdS space induces nontrivial thermodynamic geometry

BTZ black hole's thermodynamic geometry is trivial

Cosmological constant as a parameter yields no significant results

Abstract

We investigate thermodynamic geometries of two families of asymptotically Anti-de Sitter black holes, i.e. the Reissner-Nordstr\"om Anti-de Sitter in four dimensions and the BTZ black hole. It is found that the Anti-de Sitter space renders the geometry nontrivial (c.f. the Reissner-Nordstr\"om black hole in asymptotically flat background). The BTZ black hole's thermodynamic geometry is trivial despite the fact that it is characterized by the (negative) cosmological constant. As a matter of curiosity we compute thermodynamic geometry of these black holes regarding the cosmological constant as a true parameter but no physically significant results can be derived.