The Photogravitational Identity: A Universal Constant for Stellar Structure

We present a universal identity that unifies radiation, gravity, and relativistic compactness into a single invariant relation valid for all self-luminous stellar objects. By introducing the photogravitational parameter Φ ≡ L/(Mg) and combining it with relativistic compactness β ≡ GM/(Rc²), we derive the identity I ≡ Φβ²/(T⁴R²) = 4πGσ/c⁴, which connects fundamental constants from gravity, quantum thermodynamics, and relativity. This identity reduces stellar degrees of freedom from three to two, revealing a previously unrecognized constraint on stellar structure. Application to Wolf-Rayet stars demonstrates tight clustering of Φ by spectral subtype, enabling a new mass diagnostic that reveals a systematic 43% deficit compared to evolutionary models. This discrepancy suggests missing physics in near-Eddington stellar evolution. The identity provides both a theoretical framework spanning from main-sequence stars to black holes and practical diagnostic metrics for parameter consistency. We validate the identity using Solar parameters (agreement at 10⁻⁶ level) and provide a general relativistic extension for compact objects. This work establishes a new fundamental relationship in stellar astrophysics with implications for understanding stellar structure and evolution.