From Eddington Saturation to Black Hole Horizons – A Unified Geometric Framework

This work traces a continuous geometric pathway from the Eddington limit to the black hole horizon. By starting with the radiative–gravitational balance at a stellar photosphere and expressing it through the unified syntax of flux, acceleration, and area, we show that Eddington saturation is not merely a luminosity bound but a geometric growth law for the stellar radius. The same formal closure, when driven to the compactness limit, naturally reproduces the entropy–area scaling of horizon thermodynamics. This creates a conceptual bridge: from the expansion of an Eddington-limited star, governed by a purely geometric clock, to the static boundary of a black hole, where the surface becomes a causal horizon. In both regimes, radiation and gravity are facets of the same underlying geometry, directly measurable from surface observables.