Scalar Gravity: Einstein Equations

This lecture covers the concept of scalar gravity, starting with a recap on covariant derivatives and the Levi-Civita connection. It then delves into the Ricci tensor, Weyl tensor, and the Einstein tensor, discussing their symmetries and properties. The principle of equivalence, Einstein Equivalence Principle, and the plan for the day focusing on scalar gravity are also explained. The lecture further explores the generalization of Newtonian gravity equations to scalar gravity, emphasizing the Einstein-Hilbert action and the cosmological constant. Various exercises are presented to demonstrate the application of scalar gravity in different scenarios.