Volume integral theorem for exotic matter

Abstract

We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.

Thin-shell wormholes in dilaton gravity

“…Lorentzian four dimensional traversable wormholes in the context of low energy effective string theory or in Einstein gravity with a massless scalar field were already proposed by Kim and Kim [20], Vollick [21], Barceló and Visser [22], Bronnikov and Grinyok [23], Armendáriz-Picón [24], Graf [25], Nandi and Zhang [26], and Nandi et al [27], but, differing from our construction, in these works the energy conditions were violated in a non compact region. Moreover, as we consider a non vanishing charge, this allows for a comparison with the thin-shell wormhole associated to the Reissner-Nordström geometry [12].…”

“…Recently, there has been a growing interest in quantifying the amount of exotic matter present around the throat. Visser et al [7] showed that the exotic matter can be made infinitesimally small by appropriately choosing the geometry of the wormhole, and Nandi et al [8] proposed a precise volume integral quantifier for the average null energy condition (ANEC) violating matter. This quantifier was subsequently used by Nandi and Zhang [9] as a test of the physical viability of traversable wormholes.…”

On wormhole throats in f (R) gravity theory

“…Therefore, in this class of models, throats (and we stress again here that we are not considering asymptotics at infinity) are allowed which respect energy conditions. This will remain true even when adding the Einstein term to the action, as in the Einstein case the near-throat violation of energy conditions may be made arbitrarily small [60], [61] independently of the α 2 parameter.…”

Stability of thin-shell wormholes from noncommutative BTZ black hole

“…Though, using noncommutative BTZ black hole in the thin-shell wormhole construction is that, it is not asymptotically flat and therefore the wormholes are not asymptotically flat. Recently Mazharimousavi, Halilsoy and Amirabi [72] shown that a non-asymptotically flat black hole solution provides stable thin-shell wormholes which are entirely supported by exotic matter and quantified by the integral [73][74][75][76] where g represents the determinant of the metric tensor. Now, by introducing the radial coordinate R = r − a, we have…”