Criteria for energy conditions

Abstract

In model building studies, it is important to check the energy conditions for the corresponding energy–momentum tensor determined by the gravitational field equations in order to single out physically reasonable models. In this process, one often encounters a situation where the energy–momentum tensor has one off-diagonal ‘space–time’ component in the frame with an orthonormal basis in a given spacetime. We derive useful criteria of energy–momentum tensors for their Hawking–Ellis types and the standard energy conditions in such situations. As demonstrations, we apply those criteria to four different systems.