Classical and Semi-classical Energy Conditions

Abstract

The standard energy conditions of classical general relativity are (mostly) linear in the stress–energy tensor, and have clear physical interpretations in terms of geodesic focussing, but suffer the significant drawback that they are often violated by semi-classical quantum effects. In contrast, it is possible to develop non-standard energy conditions that are intrinsically nonlinear in the stress–energy tensor, and which exhibit much better well-controlled behaviour when semi-classical quantum effects are introduced, at the cost of a less direct applicability to geodesic focussing. In this chapter, we will first review the standard energy conditions and their various limitations. (Including the connection to the Hawking–Ellis type I, II, III, and IV classification of stress–energy tensors). We shall then turn to the averaged, nonlinear, and semi-classical energy conditions, and see how much can be done once semi-classical quantum effects are included.