Stability of Schwarzschild (Anti)de Sitter black holes in Conformal Gravity

TL;DR

This paper investigates the thermodynamic stability and phase transitions of Schwarzschild (Anti)de Sitter black holes within conformal gravity using multiple analytical methods, revealing potential phase transitions and stability regimes.

Contribution

It applies diverse thermodynamic analysis techniques to conformal gravity black holes, demonstrating the applicability of thermodynamic geometry and identifying stability conditions.

Findings

Entropy of de Sitter black holes lies between 2/3 and 1.

Thermodynamic geometry indicates a second order phase transition at entropy S=1.

Black holes with entropy S<4/3 are stable or saddle points, S>4/3 are unstable.

Abstract

We study the thermodynamics of spherically symmetric, neutral and non-rotating black holes in conformal (Weyl) gravity. To this end, we apply different methods: (i) the evaluation of the specific heat; (ii) the study of the entropy concavity; (iii) the geometrical approach to thermodynamics known as \textit{thermodynamic geometry}; (iv) the Poincar\'{e} method that relates equilibrium and out-of-equilibrium thermodynamics. We show that the thermodynamic geometry approach can be applied to conformal gravity too, because all the key thermodynamic variables are insensitive to Weyl scaling. The first two methods, (i) and (ii), indicate that the entropy of a de Sitter black hole is always in the interval $2/3\leq S\leq 1$, whereas thermodynamic geometry suggests that, at $S=1$, there is a second order phase transition to an Anti de Sitter black hole. On the other hand, we obtain from the Poincar\'{e} method (iv) that black holes whose entropy is $S < 4/3$ are stable or in a saddle-point, whereas when $S>4/3$ they are always unstable, hence there is no definite answer on whether such transition occurs.