Vacuum solution (general relativity)

More generally, a vacuum region in a Lorentzian manifold is a region in which the Einstein tensor vanishes.

Vacuum solutions are a special case of the more general exact solutions in general relativity.

The fact that the gravitational field itself possesses energy yields a way to understand the nonlinearity of the Einstein field equation: this gravitational field energy itself produces more gravity. This means that the gravitational field outside the Sun is a bit stronger according to general relativity than it is according to Newton's theory.

Several of the families mentioned here, members of which are obtained by solving an appropriate linear or nonlinear, real or complex partial differential equation, turn out to be very closely related, in perhaps surprising ways.