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Explore the mathematical framework of lightlike geodesics within Schwarzschild geometry through this 37-minute lecture from NPTEL-NOC IITM. Delve into the fundamental principles governing the paths of light rays in the curved spacetime around a spherically symmetric, non-rotating massive object as described by the Schwarzschild metric. Examine the mathematical derivation and physical interpretation of null geodesics, understanding how photons travel through the gravitational field of black holes and other massive bodies. Analyze the key equations that describe lightlike trajectories, including the effective potential for photon orbits, critical impact parameters, and the phenomenon of photon spheres. Study the relationship between lightlike and timelike geodesics in this geometric framework, building upon concepts of general relativity and differential geometry to understand how light behaves in strong gravitational fields.
