Information geometry on the space of equilibrium states of black holes in higher derivative theories

Abstract

We study the information-geometric properties of the Deser–Sarioglu–Tekin black hole, which is a higher derivative gravity solution with contributions from a non-polynomial term of the Weyl tensor to the Einstein–Hilbert Lagrangian. Our investigation is focused on deriving the relevant information metrics and their scalar curvatures on the space of equilibrium states. The analysis is conducted within the framework of thermodynamic information geometry and shows highly non-trivial statistical behavior. Furthermore, the quasilocal formalism, developed by Brown and York, was successfully implemented in order to derive the mass of the Deser–Sarioglu–Tekin black hole.