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