Criteria for energy conditions

TL;DR

This paper develops criteria for assessing energy conditions in models with off-diagonal energy-momentum tensor components, aiding in identifying physically reasonable gravitational models.

Contribution

It introduces new criteria for energy-momentum tensors with off-diagonal components, applicable to Hawking-Ellis classification and energy conditions.

Findings

Criteria successfully classify energy-momentum tensors.

Application to four systems demonstrates practical usefulness.

Enhances model building in gravitational physics.

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.