Geometric structure of the generic static traversable wormhole throat

Abstract

Traversable wormholes have traditionally been viewed as intrinsically topological entities in some multiply connected spacetime. Here, we show that topology is too limited a tool to accurately characterize a generic traversable wormhole: in general one needs geometric information to detect the presence of a wormhole, or more precisely to locate the wormhole throat. For an arbitrary static spacetime we shall define the wormhole throat in terms of a 2-dimensional constant-time hypersurface of minimal area. (Zero trace for the extrinsic curvature plus a "flare-out" condition.) This enables us to severely constrain the geometry of spacetime at the wormhole throat and to derive generalized theorems regarding violations of the energy conditions-theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the spherically symmetric Morris-Thorne traversable wormhole. [For example: the null energy condition (NEC), when suitably weighted and integrated over the wormhole throat, must be violated.] The major technical limitation of the current approach is that we work in a static spacetime-this is already a quite rich and complicated system.Comment: 25 pages; plain LaTeX; uses epsf.sty (four encapsulated postscript figures

Stability of Chaplygin gas thin-shell wormholes

“…For the case of static wormholes the throat is defined as a minimal area surface satisfying a flare-out condition [3]. To fulfill this, wormholes must be threaded by exotic matter that violates the null energy condition [1][2][3][4]; it was shown by Visser et al [5], however, that the amount of exotic matter needed around the throat can be made as small as desired by means of an appropriate choice of the geometry of the wormhole.…”

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.…”

Thin-shell wormholes in Einstein–Maxwell theory with a Gauss–Bonnet term

“…The throat is defined as a minimal area hypersurface which satisfies a flare-out condition [3]. This requires the presence of exotic matter, that is, matter which violates the null energy condition (NEC) [1,2,3,4].…”

“…The throat is defined as a minimal area hypersurface which satisfies a flare-out condition [3]. This requires the presence of exotic matter, that is, matter which violates the null energy condition (NEC) [1,2,3,4]. Because it has been shown that the amount of exotic matter necessary for the existence of a wormhole can be made infinitesimally small by a suitable choice of the geometry [5], considerable efforts have been addressed to precisely quantify such amount for different configurations, and to show how it can be minimized [6].…”