Lambdavacuum Solution - Relation With Einstein Manifolds

Relation With Einstein Manifolds

The definition of a lambdavacuum solution makes mathematical sense irrespective of any physical interpretation, and lambdavacuums are in fact a special case of a concept which is studied by pure mathematicians.

Einstein manifolds are Riemannian manifolds in which the Ricci tensor is proportional (by some constant, not otherwise specified) to the metric tensor. Such manifolds may have the wrong signature to admit a spacetime interpretation in general relativity, and may have the wrong dimension as well. But the Lorentzian manifolds which are also Einstein manifolds are precisely the Lambdavacuum solutions.