Thermodynamic Geometry of black hole in the deformed Horava-Lifshitz gravity

TL;DR

This paper explores the thermodynamic geometry and phase transitions of a Kehagias-Sfetsos black hole within deformed Horava-Lifshitz gravity, revealing insights into its microstructure and effective interactions.

Contribution

It analyzes the thermodynamic curvature and phase transition points, linking divergence of capacities to microstructure interactions in the black hole.

Findings

Thermodynamic curvature is positive for all r_+ > r_-

Divergence at η_2=0 corresponds to phase transition points

Black hole microstructure exhibits effective repulsive interactions similar to fermions

Abstract

We investigate the thermodynamic geometry and phase transition of Kehagias-Sfetsos black hole in the deformed Horava-Lifshitz gravity with coupling constant $\lambda=1$. The phase transition in black hole thermodynamics is thought to be associated with the divergence of the capacities. And the structures of these divergent points are studied. We also find that the thermodynamic curvature produced by the Ruppeiner metric is positive definite for all $r_+ > r_-$ and is divergence at $\eta_2=0$ corresponded to the divergent points of $C_{\Phi}$ and $C_T$. These results suggest that the microstructure of the black hole has an effective repulsive interaction, which is very similar to the ideal gas of fermions. These may shine some light on the microstructure of the black hole.