A Physically Consistent Model of Black Holes with Finite Density Cores

The problem of singularities in black holes remains one of the key unresolved issues in General Relativity (GR). Traditional solutions to the Einstein equations predict infinite density at the center of black holes, indicating a need for modifications to the theory. This paper presents a physically motivated model of black holes with finite-density cores, demonstrating agreement with energy conditions, stability of curvature invariants, and observable phenomena. We introduce a modified energy density, equation-of-state parameters, and pressure anisotropy, linking them to quantum effects and conditions in extreme environ ments.