The Photogravitational Parameter Φ: A Surface-First Diagnostic for Luminous Stars

We present the photogravitational parameter Φ as a practical, surface-based diagnostic for massive stars close to the Eddington limit. Unlike traditional approaches that depend on uncertain opacity models, Φ is derived directly from observable quantities—luminosity, mass, and surface gravity—making it robust and model-independent. In this work we extend the framework with general relativistic corrections, showing how spacetime curvature modifies the balance between radiation and gravity in extreme stars. Applications to Wolf–Rayet stars and Luminous Blue Variables illustrate when these corrections become relevant and how they relate to observed instabilities. The method offers a clear, testable way to connect stellar observations with fundamental physics, bridging stellar astrophysics and gravitational thermodynamics, with implications for understanding envelope stability in the most massive stars.