Spherically symmetric black holes in Gravity from Entropy and spontaneous emission

TL;DR

This work derives static and dynamical spherically symmetric black-hole solutions in Gravity from Entropy (GfE), showing that entropic corrections induce $r^{-4}$-scale perturbations to Schwarzschild geometry and deform the horizon. By solving the modified vacuum equations and extending to comoving Lemaître coordinates, the authors demonstrate a consistent mass-evolution profile that includes a constant background evaporation term and a Hawking-like $M^{-2}$ dependence at intermediate masses, all arising from purely classical responses of the modified background. The static solutions yield a horizon shift $r_h\approx r_S+\frac{\beta}{48 r_S}$ and corrections to near-horizon geometry, while observational constraints from S2 precession and the EHT shadow bound the entropic coupling to $|\beta|$ of order $r_S^2$, with shadow tests providing the strongest limits. The dynamical analysis further shows a geometric evaporation mechanism that leads to a temperature scaling $T(M)\propto M^{-1/2}$ for large $M$ and suggests the possible existence of stable remnants, underscoring the entropic origin of black-hole radiation in the GfE framework.

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.

Figures (3)

• Figure 1: A(r) and B(r) as a function of $r$ (measured in units of Schwarzchild radius $r_S$) for $\beta =1$. The solid lines correspond to numerical evaluation of equations and the dashed lines represent the series solution in equation \ref{['eq:ser']} truncated at the first correction to Schwarzchild solution.
• Figure 2: $f_{SP} = \frac{\delta \phi(\beta)}{\delta \phi_{GR}}$ for the orbit of S2 (S0-2) orbiting Sagittarius A* for different values of $\beta/r_S^2$. The shaded region is within the observed bounds. For all values of $-1<\beta<1$ theory is well within the observed bounds.
• Figure 3: Prediction for shadow diameter of Sagittarius A* as a function of parameter $\beta$. The shaded region represent observed shadow diameter measured by the Event Horizon Telescope (EHT) Collaboration.