In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically.
According to the Einstein field equation, this means that the stress–energy tensor also vanishes identically, so that no matter or non-gravitational fields are present.
Vacuum solutions are also distinct from the lambdavacuum solutions, where the only term in the stress–energy tensor is the cosmological constant term (and thus, the lambdavacuums can be taken as cosmological models).
However, determining the precise location of this gravitational field energy is technically problematical in general relativity, by its very nature of the clean separation into a universal gravitational interaction and "all the rest".
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.
Well-known examples of explicit vacuum solutions include: These all belong to one or more general families of solutions: 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.
In addition to these, we also have the vacuum pp-wave spacetimes, which include the gravitational plane waves.