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 non-linear 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.

Regular Black Holes with Asymptotically Minkowski Cores

“…We see that ρ is maximised at coordinate location r = a 4 . Let us now analyse the various energy conditions [49][50][51][52][53][54][55][56][57][58][59][60] and see whether they are violated in our spacetime.…”

Decomposition of the total stress energy for the generalized Kiselev black hole

“…Furthermore, the Kiselev black holes, being surrounded by matter, can be viewed as examples of "dirty" black holes [6,7]. Depending on the specific parameters of the Kiselev geometry, we shall show that this matter can and often does violate the null energy condition (NEC), with potentially serious implications in terms of instability and other unusual behaviour [8][9][10][11][12][13][14][15][16][17][18][19].…”

“…so the null energy condition (NEC) is either satisfied or violated depending on the sign of the constant Kw(1 + w). (For background on the classical and semi-classical energy conditions see references [8][9][10][11][12][13][14][15][16][17][18][19].) We now develop a fully-explicit case-by-case argument, based on the sign of the constant Kw(1 + w), to determine the specific form of the linear decomposition presented in equation (2.1).…”

Understanding black hole evaporation using explicitly computed Penrose diagrams

“…9 With a little justification, this seems like a reasonable claim. It is well known that quantum field theories (QFTs) violate, by small amounts, the classical energy conditions, including energy conditions intended to prevent the non-causal transfer of energy [28]. The fact that these theories violate the energy conditions is closely tied to the faster-than-causal spreading of relativistic wavepackets in the one-particle sector of QFT [50,51].…”

“…One approach to this situation is to take both the nonsingular metric and its energy condition violations seriously, assuming they provide useful insight about the physical mechanism of evaporation. Although classically unorthodox, this approach is appealing since quantum field theories are already well known to predict energy condition violations [28]. Regardless of one's view on this matter, it is useful to keep track of where and by how much energy conditions are violated in a given solution.…”