Lambdavacuum solution

Einstein field equation solution In general relativity, a lambdavacuum solution is an exact solution to the Einstein field equation in which the only term in the stress–energy tensor is a cosmological constant term. This can be interpreted physically as a kind of classical approximation to a nonzero vacuum energy. These are discussed here as distinct from the vacuum solutions in which the cosmological constant is vanishing. Definition The Einstein field equation is often written as G a b + Λ g a b = κ T a b , {\displaystyle G_{ab}+\Lambda \,g_{ab}=\kappa \,T_{ab},} with a so-called cosmological constant term ⁠ Λ g a b {\displaystyle \Lambda \,g_{ab}} ⁠. However, it is possible to move this term to the right hand side and absorb it into the stress–energy tensor ⁠ T a b {\displaystyle T^{ab}} ⁠, so that the cosmological constant term becomes just another contribution to the stress–energy tensor. When other contributions to that tensor vanish, the result G a b = − Λ g a b {\displaystyle G_{ab}=-\Lambda \,g_{ab}} is a lambdavacuum. An equivalent formulation in terms of the Ricci tensor is R a b = Λ g a b {\displaystyle R_{ab}=\Lambda g_{ab}} in space-time dimension