Spherically symmetric black holes in Gravity from Entropy and spontaneous emission

TL;DR

This paper explores spherically symmetric black holes within the Gravity from Entropy framework, revealing perturbative corrections to Schwarzschild geometry, consistent strong-field predictions, and classical-like Hawking radiation behavior.

Contribution

It introduces a modified vacuum solution in GfE, showing perturbative corrections, mass evolution, and classical Hawking radiation without quantum assumptions.

Findings

Schwarzschild geometry receives $r^{-4}$ corrections.

GfE predicts a constant vacuum evaporation rate.

Standard Hawking mass-loss law is recovered at intermediate scales.

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 $ -\beta/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.