Most proposed curvature-regular black hole metrics still contain thermodynamic Davies points, and only specially constructed families are both curvature-regular and thermodynamically regular.
Padmanabhan, Classical and Quantum Gravity 19, 5387 (2002)
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Doubly regular black holes
Most proposed curvature-regular black hole metrics still contain thermodynamic Davies points, and only specially constructed families are both curvature-regular and thermodynamically regular.