Gravity and Geometry: Exploring Einstein's Equations

This lecture delves into the theory of general relativity, where gravity is described as the warping of spacetime. It covers Einstein's field equations, the cosmological constant, and the dynamical viewpoint of the Einstein equations. The instability of Anti-de Sitter spacetime and the AdS instability conjecture are discussed, along with alternative approaches and spherically symmetric models. The lecture concludes with the AdS instability via beam interactions and open questions regarding the collapse of AdS perturbations into black holes.