Rotating Lee-Wick Black Hole and Thermodynamics

TL;DR

This paper derives a rotating Lee-Wick black hole solution in higher-derivative gravity, analyzing its thermodynamics, stability, and phase transitions, revealing conditions for stability and the nature of its thermodynamic behavior.

Contribution

It presents the first singular rotating Lee-Wick black hole solution and explores its thermodynamic properties and phase transition behavior.

Findings

Black hole is unstable at small horizon radius.

Black hole is stable at large horizon radius.

Phase transition occurs at divergence point with maximum temperature.

Abstract

We derive a singular solution for the rotating counterpart of Lee-Wick gravity having a point source in a higher-derivative theory. We critically analyze the thermodynamics of such a thermal system by evaluating mass parameters, angular velocity, and Hawking temperature. The system follows the first law of thermodynamics and leads to the expression of entropy. We further discuss the stability and phase transition of the theory by evaluating heat capacity and free energy. The phase transition occurs at the point of divergence and the temperature is maximum. Remarkably, the black hole is unstable for a small horizon radius and stable for a large horizon radius.