Regular Harmonic Black Holes: Derivation from a Limiting-Curvature Scalar Action

This paper presents a minimal field-theoretic derivation of regular black holes within the Harmonic Curvature Model (HCM). By augmenting General Relativity with a scalar field subject to a limiting-curvature potential $V(\Phi) \propto \ln(\cosh \Phi)$, we demonstrate that the energy-momentum tensor naturally saturates at high densities. This mechanism resolves the Schwarzschild singularity, replacing it with a stable de Sitter-like core. We derive the static spherically symmetric solution, proving it corresponds to a Hayward-like metric. Stability analysis confirms that the solution avoids ghost instabilities while violating the Strong Energy Condition as required for regularity. Thermodynamics analysis predicts the formation of zero-temperature remnants, and we identify distinct observational signatures, including expanded shadows and power-law ringdown tails, testable by LIGO O5+ and ngEHT.

Keywords

Regular Black Holes, Modified Gravity, Singularity Resolution, Scalar-Tensor Theory, Limiting Curvature, Gravitational Waves, Black Hole Thermodynamics, Black Hole Shadows