GENERAL RELATIVITY

Abstract

Einstein’s General Theory of Relativity (GR) redefines gravity as the curvature of spacetime generated by mass and energy rather than a classical force. This paper analyzes the motion of photons in curved spacetime as a direct diagnostic of gravitational field dynamics within the framework of the Schwarzschild metric. The study derives and interprets the null geodesic equations for photons and evaluates measurable consequences such as light deflection, gravitational redshift, and Shapiro time delay. Analytical modeling and comparative interpretation with modified gravity theories, including f(R) and scalar–tensor frameworks, reveal how photon trajectories serve as a sensitive probe of spacetime curvature. The results reproduce Eddington’s 1919 solar deflection measurements and confirm the geometric nature of gravitation while providing a theoretical basis for testing deviations from Einstein’s predictions in strong-field regimes. This approach offers an integrative view of photon dynamics as an experimental bridge between General Relativity and extended gravity theories.