Semiclassical energy conditions for quantum vacuum states

Abstract

We present and develop several nonlinear energy conditions suitable for use in the semiclassical regime. In particular, we consider the recently formulated "flux energy condition" (FEC), and the novel "trace-of-square" (TOSEC) and "determinant" (DETEC) energy conditions. As we shall show, these nonlinear energy conditions behave much better than the classical linear energy conditions in the presence of semiclassical quantum effects. Moreover, whereas the quantum extensions of these nonlinear energy conditions seem to be quite widely satisfied as one enters the quantum realm, at least for quantum vacuum states, analogous quantum extensions are generally not useful for the linear classical energy conditions.

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

“…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).…”

“…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].…”

Phantom singularities and their quantum fate: general relativity and beyond—a CANTATA COST action topic

“…Moreover, noting that negative energies in one region of the spacetime seem to be overcompensated by positive energies in other regions, the related quantum interest conjecture was formulated [33] (see also [31,32] and references therein for developments). Apart from that, following a local point-wise approach, nonlinear ECs were formulated [34]. The most interesting example is the flux energy condition (FEC) that requires energy of any sign to propagate in a causal way as seen by any observer.…”