Traversable Wormholes with Arbitrarily Small Energy Condition Violations

Abstract

Traversable wormholes necessarily require violations of the averaged null energy condition; this being the definition of "exotic matter". However, the theorems which guarantee the energy condition violation are remarkably silent when it comes to making quantitative statements regarding the "total amount" of energy condition violating matter in the spacetime. We develop a suitable measure for quantifying this notion, and demonstrate the existence of spacetime geometries containing traversable wormholes that are supported by arbitrarily small quantities of "exotic matter".

Oxidised cosmic acceleration

“…But, even if such terms prevent pathologies, by repackaging all of the higher-derivative terms on one side of the field equations and the Einstein tensor on the other, we obtain an "effective" stress-energy which violates the NEC. This means that a variety of exotic solutions to Einstein's equations which require NEC-violating matter could potentially be permitted [37,38,39,40,45,46,47,48], but this must be checked on a case-by-case basis. It would be interesting if we were forced to accept the possibility of exotic solutions of Einstein's equations, or modifications to gravity, from observations that the universe is currently accelerating.…”

“…There are some rigorous formulations of this belief, where NEC violation is shown to lead to superluminal propagation, instabilities, and violations of unitarity or causality [30,31,32,33,34,35,36]. Certainly the NEC forbids a number of solutions to Einstein's equations with strange properties: traversable wormholes [37,38], superluminal "warp drives" [39,40,41,42,43,44], time machines [45,46], universes with big rip singularities [47,48], and pathologies with gravitational thermodynamics [49,50,51,52,53] are possible with NECviolating "exotic" matter. 2 (If one considers non-Einstein gravity, these conclusions may differ: for example, the NEC can be violated by a scalar field in Brans-Dicke gravity in Jordan frame [54] without allowing wormholes [55]).…”

Thin-shell wormholes with charge in F(R) gravity

“…In General Relativity, they are threaded by matter that violates the null energy condition [1][2][3][4][5]; the amount of this exotic matter can be made arbitrary small [6], but at the expense of large pressures at the throat [7]. Traversable wormholes can be constructed [2] by cutting and pasting two manifolds to form a new one, with a shell at the joining surface corresponding to the throat, where the flare-out condition is fulfilled.…”

Traversable wormholes: Minimum violation of the null energy condition revisited

“…Although the inevitability of violation of NEC is well known in physics of wormholes, the extent to which it occurs is still being debated in literature. It was stated in [2] that amount of exotic matter needed to support wormholes can be made as small as one likes (see also [4] - [7]). Let we have the sequence of traversable wormholes depending of some parameter ε such that in the limit ε → 0 the amount of exotic material tends to zero.…”

“…Let we have the sequence of traversable wormholes depending of some parameter ε such that in the limit ε → 0 the amount of exotic material tends to zero. According to [2], one is inclined to think that a configuration with arbitrary small but non-zero ε represents an usual traversable wormhole and, thus, some kind of discontinuity happens that separates the state with ε = 0 from those with ε = 0. By itself, this does not necessarily mean something wrong since topological properties of the configuration with ε = 0 and ε = 0 are qualitatively different, so one may or may not expect discontinuity.…”