Spherically symmetric black holes in Gravity from Entropy and spontaneous emission

Abstract: We investigate static and dynamical spherically symmetric black hole solutions within the Gravity from Entropy (GfE) framework. We derive and solve the modified vacuum field equations for a static, spherically symmetric spacetime, revealing that the classical Schwarzschild geometry receives perturbative corrections scaling as $r^{-4}$. We establish that the GfE framework is consistent with current strong-field astrophysical observations. Higher-order geometric stresses inherent to the GfE vacuum drive a consistent mass-evolution profile. In the limit of large black hole mass, the theory predicts a constant background evaporation rate $ -β/24$, suggesting an inherent "entropic leakage" of the vacuum. At intermediate scales, the framework replicates the standard Hawking radiation mass-loss law as $\dot{M} \propto M^{-2}$ through a purely classical response of the modified background.