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.

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• Classical black holes
• Singularities In general relativity
• Thermodynamics