Black hole thermodynamics in asymptotically safe gravity

TL;DR

This paper explores the thermodynamics and phase transitions of quantum-corrected asymptotically safe Schwarzschild black holes, revealing stable states, the absence of Hawking-Page transitions, and the influence of quantum corrections on thermodynamic properties.

Contribution

It introduces a detailed analysis of black hole thermodynamics incorporating quantum gravitational corrections within the asymptotic safety framework, highlighting new stability and phase transition features.

Findings

Existence of three thermodynamic black hole states with stability properties.

No Hawking-Page phase transition occurs in this quantum-corrected scenario.

Identification of two critical temperatures for phase transitions between black hole states.

Abstract

We have investigated the black hole thermodynamics and the phase transition for renormalized group improved asymptotically safe Schwarzschild black hole. This geometry takes into account the quantum gravitational correction in the running gravitational constant identifying $G(r) \equiv G(k=k(r))$. We studied various thermodynamic quantity like the Hawking temperature, specific heat and entropy for the general parameter $\gamma$ for quantum corrected Schwarzschild metric. We have noticed that the coefficient of the leading quantum correction, that is, the logarithmic correction gets affected by the presence of $\gamma$. We further study the local temperature, thermal stability of the black hole and the free energy considering a cavity enclosing the black hole. According to the local specific heat, there exists three black hole states, among them the large and tiny black hole are thermally stable states. We further investigate the on-shell free energy and find that no Hawking-Page phase transition occurs here unlike the ordinary Schwarzschild black hole. The black hole state always prevails for all temperatures. Also, we have found two critical points, $T_{c1}$ and $T_{c2}$, corresponding to the phase transition from one black hole state to another.