A Minkowski-core black hole with cosmological constant and electric charge

Within a covariant effective Hamiltonian framework, we employ an inverse construction to derive the gravitational Hamiltonian constraint for a Minkowski-core regular black hole without invoking exotic matter. We then extend the constraint by coupling it to a spherically reduced Maxwell field and including a cosmological constant. The resulting charged anti-de Sitter (AdS) and de Sitter (dS) solution is gauge independent and reduces to the Reissner--Nordstr\"om--AdS (RN-AdS) black hole when the regularization parameter vanishes. Electric charge and a cosmological constant preserve the Minkowski core: the metric approaches the Minkowski geometry at the center, the Kretschmann scalar vanishes there, and the spacetime exhibits a multi-horizon structure. Focusing on AdS backgrounds, we investigate the black hole thermodynamics. For a regularization parameter below a critical value, the model exhibits a phase transition with consistent signatures across these thermodynamic quantities, demonstrating that Minkowski-core regularization can preserve center regularity while modifying the AdS thermodynamic phase structure relative to the RN-AdS benchmark.