Vacuum solution

Summary

A vacuum solution is a spacetime that satisfies the Einstein field equations with no matter and no cosmological constant. In four dimensions this means that the Ricci curvature of the metric vanishes, so the only curvature left is the Weyl tensor. Vacuum solutions describe the gravitational field outside stars and black holes and gravitational waves in empty space. Minkowski space, the Schwarzschild metric and the Kerr metric are vacuum solutions.