Energy Momentum Tensor: Derivation and Conservation

This lecture covers the derivation of the energy momentum tensor for point particles, focusing on the covariant derivative and conservation. It also explores the impact of adding an electromagnetic field, computing the divergence of the energy momentum tensor, and deriving the expression for the electromagnetic current. Additionally, it delves into the symmetry and static nature of generic metrics in spherically symmetric spacetimes, emphasizing the Schwarzschild metric as a solution. The exercise involves analyzing the Schwarzschild metric, identifying problematic radii, and applying coordinate changes to investigate physical effects.