Information geometry of asymptotically AdS black holes

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.