Lambdavacuum Solution - Einstein Tensor

Einstein Tensor

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).

Remarkably, in the case of lambdavacuum, all observers measure the same energy density and the same (isotropic) pressure. That is, the Einstein tensor takes the form

Saying that this tensor takes the same form for all observers is the same as saying that the isotropy group of a lambdavacuum is SO(1,3), the full Lorentz group.