Information Geometry on the Space of Equilibrium States of Black Holes in Higher Derivative Theories

TL;DR

This paper explores the thermodynamic information geometry of a higher derivative black hole solution, revealing complex statistical behavior and deriving its mass using the quasilocal formalism.

Contribution

It introduces the information geometric analysis of the Deser-Sarioglu-Tekin black hole, a higher derivative gravity solution, and applies the Brown-York formalism to compute its mass.

Findings

Highly non-trivial statistical behavior observed

Derived the scalar curvature of the information metric

Successfully computed black hole mass using quasilocal formalism

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.