Topological black holes in Einstein-Maxwell and 4D conformal gravities revisited

TL;DR

This paper revisits the thermodynamics of topological black holes in Einstein-Maxwell and conformal gravities, introducing subsystems to better understand their behaviors and exploring implications for gravity models.

Contribution

It introduces the concept of subsystems for black holes, enabling detailed thermodynamic analysis of non-compact black holes with various horizon geometries in different gravity theories.

Findings

Black holes can reach zero entropy with non-zero temperature, challenging physical intuition.

At high temperatures, TBHs behave like phonon gases; at low temperatures, they resemble degenerate electron gases.

Subsystem analysis clarifies thermal fluctuation descriptions and their relative magnitudes.

Abstract

The thermodynamics of charged topological black holes (TBHs) with different horizon geometries in $d$-dimensional Einstein-Maxwell and 4-dimensional conformal gravities is revisited using the restricted phase space formalism. The concept of subsystems for black holes is introduced, which enables a precise description for the thermodynamic behaviors of (non-compact) black holes with infinitely large horizon area. The concrete behaviors can be different for TBHs in the same underlying theory but with different horizon geometries, or for those with the same horizon geometry but from different underlying theories. In some concrete thermodynamic processes, the non-compact black holes in 4-dimensional conformal gravity can reach certain state with zero entropy but nonvanishing temperature, which is physically unsounded. This suggests a novel use of black hole thermodynamics as a tool for testing the viability of gravity models or constraining the model parameters or integration constants. The high and low temperature limits of the TBHs are also considered, and it is found that, at high temperature, all TBHs behave like low temperature phonon gases, while at low temperature, all charged as well as neutral hyperbolic TBHs in Einstein-Maxwell gravity behave like strongly degenerated electron gases. Finally, using the concept of subsystems, some conceptual issues in the description for thermal fluctuations in black hole systems are clarified, and the relative thermal fluctuations for finite subsystems are also analyzed in some detail.