# Thermal stability of a special class of black hole solutions in F(R) gravity

## TL;DR

This paper explores the thermodynamic stability and phase transition behaviors of topological Lifshitz-like black holes in a specific class of F(R) gravity, revealing van der Waals-like behavior and phase transitions including negative temperature states.

## Contribution

It introduces a detailed analysis of the thermodynamic properties of Lifshitz-like black holes in F(R) gravity, highlighting phase transitions and stability features not previously studied.

## Key findings

- Van der Waals-like behavior in AdS black holes
- Phase transition with negative temperature for hyperbolic horizons
- Thermodynamic stability analyzed via P-v, G-T, and C-Q diagrams

## Abstract

In this paper, we work on the topological Lifshitz-like black hole solutions of a special class of vacuum $F(R)-$gravity that are static and spherically symmetric. We investigate geometric and thermodynamic properties of the solutions with due respect to the validity of the first law of thermodynamics. We examine the van der Waals like behavior for asymptotically AdS solutions with spherical horizon by studying the $P-v$, $G-T$ and $C_{Q,P}-r_{+}$ diagrams and find a consistent result. We also investigate the same behavior for hyperbolic horizon and interestingly find that the system under study can experience a phase transition with negative temperature.