Doubly regular black holes

TL;DR

This paper investigates the thermodynamic regularity of black hole solutions, introducing the concept of doubly regular black holes that are regular in both physical and phase space, with implications for astrophysical models.

Contribution

It presents a framework for analyzing thermodynamic regularity of black holes and introduces the concept of doubly regular black holes, especially considering angular momentum effects.

Findings

Many static, asymptotically flat black holes are not thermodynamically regular in phase space.

Including angular momentum via the Newman-Janis algorithm restricts the class of doubly regular black holes.

Thermodynamic regularity can help narrow down viable regular black hole models.

Abstract

In addition to curvature singularities, electrovacuum black holes in general relativity exhibit thermodynamic singularities. These so-called Davies' points occur at nonextremal values of charge and spin where the heat capacity diverges and may indicate a type of theoretical incompleteness. The thermodynamic regularity of several families of static, asymptotically flat spacetimes with bounded curvature invariants is examined using a theory-agnostic framework, showing that, while they may be regular in physical space, they are generally not in phase space. The inclusion of angular momentum, via the Newman-Janis algorithm, makes the set of such "doubly regular" objects especially restrictive. It is argued that, if thermodynamic regularity is to be considered a desirable property for an astrophysical black hole, these considerations could be used to narrow down the viable pool of regular extensions to the Kerr-Newman metric.