Two-dimensional Lifshitz-like AdS black holes in $F(R)$ gravity

TL;DR

This paper derives and analyzes two-dimensional Lifshitz-like AdS black hole solutions within $F(R)$ gravity, examining their thermodynamic properties, stability, and connections to known black hole solutions, revealing phase transitions and conditions for physicality.

Contribution

It introduces new 2D Lifshitz-like AdS black hole solutions in $F(R)$ gravity and explores their thermodynamic stability and relation to existing black hole models.

Findings

Black hole solutions have an essential singularity at r=0 covered by an event horizon.

Stable solutions exist for negative cosmological constant and large radii.

Phase transition occurs between stable and unstable black hole states.

Abstract

Two-dimensional ($2D$) Lifshitz-like black holes in special $F(R)$ gravity cases are extracted. We indicate an essential singularity at $r=0$, covered with an event horizon. Then conserved and thermodynamic quantities such as temperature, mass, entropy, and the heat capacity of $2D$ Lifshitz-like black holes in $F(R)$ gravity are evaluated. Our analysis shows that $2D$ Lifshitz-like black hole solutions can be physical solutions, provided that the cosmological constant is negative ($\Lambda<0$). Indeed, there is a phase transition between stable and unstable cases by increasing the radius of AdS black holes. In other words, the $2D$ Lifshitz-like AdS black holes with large radii are physical and enjoy thermal stability. The obtained $2D$ Lifshitz-like AdS-black holes in $F(R)$ gravity turn to the well-known $2D$ Schwarzschild AdS-black holes when the Lifshitz-like parameter is zero ($s=0$). Also, correspondence between these black hole solutions and the $2D$ rotating black hole solutions is found by adjusting the Lifshitz-like parameter.