A Primer on Energy Conditions

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.

References in corpus (15)

• Traversable wormholes: Some simple examples
• Traversable wormholes from surgically modified Schwarzschild spacetimes
• Singularity Theorems and Their Consequences
• Energy conditions in the epoch of galaxy formation
• Energy conditions bounds on f(T) gravity
• Spherical black holes with regular center: a review of existing models including a recent realization with Gaussian sources
• Dynamical laws of superenergy in General Relativity
• Barotropic index w-singularities in cosmology
• Raiders of the lost spacetime
• Cosmological Singularities and Bel-Robinson Energy
• Cosmodynamics: Energy conditions, Hubble bounds, density bounds, time and distance bounds
• A singularity theorem based on spatial averages
• Cosmological milestones and energy conditions
• Measure, Topology and Probabilistic Reasoning in Cosmology
• A New Type of Singularity Theorem

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