Constraints and Consistency of Rotating Regular Black Hole Thermodynamics

Abstract

The thermodynamics of regular black holes has long suffered from a self-consistency problem: the Hawking temperature derived from the first law disagrees with the geometrically defined one, signaling that the thermodynamic quantities obtained in previous studies are unreliable. To resolve this, we construct a rotating ``mother'' black hole whose parameters are initially independent, forming an extended thermodynamic phase space. Thermodynamic quantities are first derived in this unconstrained phase space, and only then is the regularity condition imposed. We find a fundamental asymmetry between the geometric and thermodynamic derivations: the geometric temperature is invariant under the order of constraint application, whereas the thermodynamic temperature requires the correct order of operations to yield a physically meaningful result. This establishes a self-consistent thermodynamic framework for rotating regular black holes, in which all thermodynamic quantities are guaranteed to be physically correct, laying a rigorous foundation for investigating phase transitions and thermodynamic stability.