Geometric structure of the generic static traversable wormhole throat

Details Geometric structure of the generic static traversable wormhole throat Geometric structure of the generic static traversable wormhole throat

1997-04-29

arxiv.org/abs/gr-qc/9704082v1

Phys.Rev.D56:4745-4755,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages; plain LaTeX; uses epsf.sty (four encapsulated postscript figures)

Scientific paper

10.1103/PhysRevD.56.4745

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.

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