General Relativity: Einstein Equations

This lecture covers the Lagrangian formulation of General Relativity, introducing the Einstein-Hilbert action and deriving the Einstein equations in vacuum. It discusses the Newtonian limit, scalar gravity, and the minimal-coupling principle, leading to the generalization of the gravitational field equations. The instructor explains the concepts of geodesic equations and the independence of photon trajectories from the mass density. The lecture concludes with a detailed analysis of the Einstein equations and their implications in the context of General Relativity.