A Primer on Energy Conditions

TL;DR

This paper reviews energy conditions in spacetime theories, highlighting their importance, the lack of understanding of their nature, and analyzing their technical and conceptual aspects and implications.

Contribution

It provides a detailed analysis of the standard energy conditions, exploring their theoretical status, physical interpretation, and circumstances of violation.

Findings

Energy conditions have profound implications for spacetime structure.

There is limited understanding of the fundamental nature of energy conditions.

Standard energy conditions are often violated in physical scenarios.

Abstract

An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated.