Einstein field equations

Summary

The Einstein field equations are the equations of general relativity. They relate the curvature of a four-dimensional Lorentzian manifold, the spacetime, to the energy and momentum of matter in it. For the metric they form a system of nonlinear second-order partial differential equations, which is hyperbolic after a suitable choice of coordinates. Their solutions include the flat Minkowski space, the Schwarzschild black hole and the expanding cosmological models.