Lambdavacuum 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. Terminological note: this article concerns a standard concept, but there is apparently no standard term to denote this concept, so we have attempted to supply one for the benefit of Wikipedia. The Einstein field equation is often written as with a so-called cosmological constant term . However, it is possible to move this term to the right hand side and absorb it into the stress–energy tensor , so that the cosmological constant term becomes just another contribution to the stress–energy tensor. When other contributions to that tensor vanish, the result is a lambdavacuum. An equivalent formulation in terms of the Ricci tensor is A nonzero cosmological constant term can be interpreted in terms of a nonzero vacuum energy. There are two cases: positive vacuum energy density and negative isotropic vacuum pressure, as in de Sitter space, negative vacuum energy density and positive isotropic vacuum pressure, as in anti-de Sitter space. The idea of the vacuum having a nonvanishing energy density might seem counterintuitive, but this does make sense in quantum field theory. Indeed, nonzero vacuum energies can even be experimentally verified in the Casimir effect. The components of a tensor computed with respect to a frame field rather than the coordinate basis are often called physical components, because these are the components which can (in principle) be measured by an observer. A frame consists of four unit vector fields Here, the first is a timelike unit vector field and the others are spacelike unit vector fields, and is everywhere orthogonal to the world lines of a family of observers (not necessarily inertial observers).