# Thermodynamic Stability of the Stationary Lifshitz Black Hole of New Massive Gravity

## TL;DR

This paper analyzes the thermodynamic stability and phase transitions of a Lifshitz black hole solution in New Massive Gravity using thermodynamic geometry and geodesic analysis.

## Contribution

It introduces a detailed thermodynamic geometric framework to study stability and phase transitions of Lifshitz black holes in New Massive Gravity.

## Key findings

- Identification of parameter space restrictions for stability
- Detection of phase transition points via curvature invariants
- Confirmation of phase transitions through geodesic analysis

## Abstract

In this paper we investigate the thermodynamic properties of the stationary Lifshitz black hole solution of New Massive Gravity. We study the thermodynamic stability from local and global point of view. We also consider the space of equilibrium states for the solution within the framework of Thermodynamic Information Geometry. By investigating the proper thermodynamic metrics and their curvature invariants we find a set of restrictions on the parameter space and the critical points indicating phase transitions of the system. We confirm our findings by analytical analysis of the geodesics on the space of equilibrium states.