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Title: Dynamic wormholes, antitrapped surfaces, and energy conditions

Abstract

It is by now apparent that topology is too crude a tool to accurately characterize a generic traversable wormhole. In two earlier papers we developed a complete characterization of generic but static traversable wormholes, and in the present paper extend the discussion to arbitrary time-dependent (dynamical) wormholes. A local definition of a wormhole throat, free from assumptions about asymptotic flatness, symmetries, future and past null infinities, embedding diagrams, topology, and even time dependence is developed that accurately captures the essence of what a wormhole throat is, and where it is located. Adapting and extending a suggestion due to Page, we define a wormhole throat to be a marginally anti-trapped surface, that is, a closed two-dimensional spatial hypersurface such that one of the two future-directed null geodesic congruences orthogonal to it is just beginning to diverge. Typically a dynamic wormhole will possess {ital two} such throats, corresponding to the two orthogonal null geodesic congruences, and these two throats will not coincide (though they do coalesce into a single throat in the static limit). The divergence property of the null geodesics at the marginally anti-trapped surface generalizes the {open_quotes}flare-out{close_quotes} condition for an arbitrary wormhole. We derive theorems regarding violations of the nullmore » energy condition (NEC) at and near these throats and find that, even for wormholes with arbitrary time dependence, the violation of the NEC is a generic property of wormhole throats. We also discuss wormhole throats in the presence of fully antisymmetric torsion and find that the energy condition violations {ital cannot} be dumped into the torsion degrees of freedom. Finally by means of a concrete example we demonstrate that even temporary suspension of energy-condition violations is incompatible with the flare-out property of dynamic throats. {copyright} {ital 1998} {ital The American Physical Society}« less

Authors:
 [1];  [2]
  1. Laboratorio de Astrofisica Espacial y Fisica Fundamental, Apartado 50727, 28080 Madrid (Spain)
  2. Physics Department, Washington University, Saint Louis, Missouri 63130-4899 (United States)
Publication Date:
OSTI Identifier:
639850
Resource Type:
Journal Article
Journal Name:
Physical Review, D
Additional Journal Information:
Journal Volume: 58; Journal Issue: 4; Other Information: PBD: Aug 1998
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; COSMOLOGY; SURFACES; ENERGY; TIME DEPENDENCE; TORSION; DYNAMICS; TOPOLOGY; MINKOWSKI SPACE; SPACE-TIME

Citation Formats

Hochberg, D, and Visser, M. Dynamic wormholes, antitrapped surfaces, and energy conditions. United States: N. p., 1998. Web. doi:10.1103/PhysRevD.58.044021.
Hochberg, D, & Visser, M. Dynamic wormholes, antitrapped surfaces, and energy conditions. United States. https://doi.org/10.1103/PhysRevD.58.044021
Hochberg, D, and Visser, M. 1998. "Dynamic wormholes, antitrapped surfaces, and energy conditions". United States. https://doi.org/10.1103/PhysRevD.58.044021.
@article{osti_639850,
title = {Dynamic wormholes, antitrapped surfaces, and energy conditions},
author = {Hochberg, D and Visser, M},
abstractNote = {It is by now apparent that topology is too crude a tool to accurately characterize a generic traversable wormhole. In two earlier papers we developed a complete characterization of generic but static traversable wormholes, and in the present paper extend the discussion to arbitrary time-dependent (dynamical) wormholes. A local definition of a wormhole throat, free from assumptions about asymptotic flatness, symmetries, future and past null infinities, embedding diagrams, topology, and even time dependence is developed that accurately captures the essence of what a wormhole throat is, and where it is located. Adapting and extending a suggestion due to Page, we define a wormhole throat to be a marginally anti-trapped surface, that is, a closed two-dimensional spatial hypersurface such that one of the two future-directed null geodesic congruences orthogonal to it is just beginning to diverge. Typically a dynamic wormhole will possess {ital two} such throats, corresponding to the two orthogonal null geodesic congruences, and these two throats will not coincide (though they do coalesce into a single throat in the static limit). The divergence property of the null geodesics at the marginally anti-trapped surface generalizes the {open_quotes}flare-out{close_quotes} condition for an arbitrary wormhole. We derive theorems regarding violations of the null energy condition (NEC) at and near these throats and find that, even for wormholes with arbitrary time dependence, the violation of the NEC is a generic property of wormhole throats. We also discuss wormhole throats in the presence of fully antisymmetric torsion and find that the energy condition violations {ital cannot} be dumped into the torsion degrees of freedom. Finally by means of a concrete example we demonstrate that even temporary suspension of energy-condition violations is incompatible with the flare-out property of dynamic throats. {copyright} {ital 1998} {ital The American Physical Society}},
doi = {10.1103/PhysRevD.58.044021},
url = {https://www.osti.gov/biblio/639850}, journal = {Physical Review, D},
number = 4,
volume = 58,
place = {United States},
year = {Sat Aug 01 00:00:00 EDT 1998},
month = {Sat Aug 01 00:00:00 EDT 1998}
}