Regular black holes and complete monotonicity

We examine the conjecture for the complete monotonicity of certain curvature invariants for regular black holes. In this note, we study a class of regular black holes that are static, spherically symmetric, and characterized only by their mass. We introduce a large class of space times of this type, which is compatible with the complete monotonicity conjecture. Additionally, this class of black holes reduces to the Schwarzschild solution in the classical limit ℏ → 0. We demonstrate that these regular black holes cannot be generated by perturbative quantum corrections to the Einstein equations. We then investigate the thermodynamics of these black holes and derive a bound on their entropy, showing that the entropy is always greater than the horizon area divided by 4G. The complete monotonicity conjecture also implied that the core of the regular black hole analogue of the Schwarzschild black hole must be a de-Sitter space time.