Exact solutions in general relativity

Summary

An exact solution in general relativity is a spacetime, together with its matter fields, that satisfies the Einstein field equations exactly, without approximation. Usually it is given by an explicit formula for the metric in some coordinates. Exact solutions are found by imposing symmetries or algebraic conditions that reduce the equations to a manageable system. The Schwarzschild metric, the Kerr metric and the Friedmann–Lemaître–Robertson–Walker metric are the best known, and they model black holes and the expanding universe.