Energy conditions in arbitrary dimensions

TL;DR

This paper systematically classifies energy-momentum tensors in arbitrary dimensions and establishes conditions under which various energy conditions hold or are violated, enhancing understanding of matter fields in higher-dimensional spacetimes.

Contribution

It introduces a new classification of energy-momentum tensors in arbitrary dimensions and provides criteria for energy condition validity, including analysis of physically motivated matter fields.

Findings

Type III energy-momentum tensors are more clearly defined.

Types III and IV violate all standard energy conditions.

Necessary and sufficient inequalities for types I and II are established.

Abstract

Energy conditions for matter fields are comprehensively investigated in arbitrary $n(\ge 3)$ dimensions without specifying future and past directions locally. We classify an energy-momentum tensor into $n$-dimensional counterparts of the Hawking-Ellis type I to IV, where type III is defined by a more useful form than those adopted by Hawking and Ellis and other authors to identify the type-III energy-momentum tensor in a given spacetime. We also provide necessary and sufficient conditions for types I and II as inequalities for the orthonormal components of the energy-momentum tensor in a canonical form and show that types III and IV violate all the standard energy conditions. Lastly, we study energy conditions for a set of physically motivated matter fields.