Kuznetsov–bardeen Regular Black Hole From Entropy Field Action

Abstract We propose a modified gravitational model where the regular Bardeen-Hayward black hole geometry emerges naturally from the dynamics of an entropy field S. The model is based on the gravitational action Varying this action with respect to the metric yields modified Einstein equations with an effective stress-energy tensor sourced by the entropy field. We identify the coarse-grained form of this tensor with the Kuznetsov tensor Kμν, providing a fundamental origin for the de Sitter core and resolving the singularity problem. We derive the spherically symmetric solution, demonstrating that all curvature invariants remain finite at the origin, thus proving the regularity of the spacetime. The thermodynamic analysis reveals a rich structure: we calculate the black hole mass as a function of the horizon radius, determine the Hawking temperature, and analyze the heat capacity. A key prediction of the model is the existence of a thermodynamically stable remnant state with zero Hawking temperature, corresponding to a second-order phase transition in the evaporation process. This feature offers a natural framework for addressing the information loss paradox, as information may be preserved within the finite-size de Sitter core generated by the entropy field dynamics. Our approach provides a novel connection between entropy, geometry, and quantum gravity effects, derived from a fundamental action principle.