General Relativistic Extension of the Exponential Radius Law Near the Eddington Limit

This work introduces a surface-based photogravitational framework that unifies radiation and gravity through the parameter Φ = L/(M g), evaluated near the Eddington limit. By relying exclusively on observable surface quantities, the method avoids dependence on interior stellar models while remaining compatible with stellar evolution codes such as MESA. The framework incorporates opacity effects (including OPAL tables), relativistic corrections, and dynamical processes such as mass loss and winds.

The principal outcome is a modified exponential law for stellar radius evolution, applicable to compact stars in near-Eddington regimes. As Φ approaches its boundary value in strong-field domains, the framework indicates deeper connections with horizon thermodynamics and suggests a potential conceptual bridge to quantum gravity. It thereby provides both a practical diagnostic for stellar structure and a unifying theoretical perspective spanning classical and relativistic regimes.