Energy conditions in arbitrary dimensions

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.

46 pages, 1 table, no figure; v5, final version to appear in Progress of Theoretical and Experimental Physics

References in corpus (5)

• Gravitational Cheshire effect: Nonminimally coupled scalar fields may not curve spacetime
• The Quantum Null Energy Condition in Curved Space
• All solutions of Einstein's equations in 2+1 dimensions: $\Lambda$-vacuum, pure radiation, or gyratons
• Generalized Rainich conditions, generalized stress-energy conditions, and the Hawking-Ellis classification
• The type III stress-energy tensor: Ugly Duckling of the Hawking-Ellis classification

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