Entropy-Deformed Hamiltonian Dynamics of Schwarzschild Black Holes: A Superstatistical Approach

We study the effective dynamics of the Schwarzschild black hole interior by introducing entropic deformations derived from generalized superstatistical entropies $S_{+}$ and $S_{-}$. The resulting modified Hamiltonians $\bar{H}_{\pm}$, formulated in Ashtekar--Barbero variables, encode quantum gravity-inspired corrections that become significant near the Planck scale. Analytical solutions show that these corrections regularize the classical singularity, replacing it with a finite anisotropic core characterized by bounded canonical variables and a minimal internal area. For $S_{-}$ ($\alpha_{-} > 0$), curvature invariants remain finite, yielding a completely regular interior, whereas $S_{+}$ ($\alpha_{+} < 0$) leads to a localized region of high curvature associated with a cigar-like throat. The interior and exterior geometries are thus connected through this high-curvature region, indicating that the classical singularity is replaced by an entropic transition layer. These features reproduce loop quantum gravity phenomenology without invoking polymer discretization.