Scalar Field 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.

In the special case of a minimally coupled massless scalar field, an adapted frame

(the first is a timelike unit vector field, the last three are spacelike unit vector fields) can always be found in which the Einstein tensor takes the simple form

where is the energy density of the scalar field.