General Relativity

General relativity is Einstein's geometric theory of gravitation, in which spacetime is a four-dimensional pseudo-Riemannian manifold and the gravitational field is encoded in the metric tensor. The Einstein field equations relate the Einstein curvature tensor to the stress-energy content of spacetime, with the cosmological constant accounting for a uniform vacuum energy density. Its empirical successes span Mercury's perihelion precession, gravitational lensing, GPS clock correction, Shapiro time delay, gravitational waves from binary inspirals, and the shadow of M87*; its open problems include reconciliation with quantum theory, the singularity theorems of Penrose and Hawking, and the cosmic-censorship conjecture.