the form Using Newton's identities, this condition can be re-expressed in terms of the traces of the powers of the Einstein tensor as where are the traces of the powers of the linear operator corresponding to the Einstein tensor, which has second rank. Relation with Einstein manifolds The definition of a lambdavacuum solution makes sense mathematically irrespective of any physical interpretation, and lambdavacuums are a special case of a concept that is studied by pure mathematicians. Einstein manifolds are pseudo-Riemannian manifolds in which the Ricci tensor is proportional to the metric tensor. The Lorentzian manifolds that are also Einstein manifolds are precisely the lambdavacuum solutions. Examples Noteworthy individual examples of lambdavacuum solutions include: de Sitter space, often referred to as the dS cosmological model, anti-de Sitter space, often referred to as the AdS cosmological model, de Sitter–Schwarzschild metric, which models a spherically symmetric massive object immersed in a de Sitter universe (and likewise for AdS), Kerr–de Sitter metric, the rotating generalization of the latter, Nariai spacetime; this is the only solution in general relativity, other than the Bertotti–Robinson electrovacuum, that has a Cartesian product structure. See also Exact solutions in general relativity Exact solutions in general relativity