Reissner-Nordström-de Sitter black holes with holonomy corrections
We investigate spherical charged black holes in a cosmological background, with corrections inspired by loop quantum gravity. An effective theory is constructed at the Hamiltonian level, ensuring that different gauge choices simply correspond to different charts of the same spacetime solution. The resulting geometry is characterized by four parameters: mass, charge, cosmological constant, and a polymerization parameter for quantum-gravity corrections. The study identifies the specific parameter ranges for singularity-free spacetimes and analyzes their global structure. To achieve a nonsingular geometry, the mass and cosmological constant must be nonnegative, and the charge must be relatively small. This model provides a globally regular description suitable for any known spherical astrophysical black hole in the de Sitter cosmological background.