1998/10/08 by David Hochberg, Carmen Molina-Paris, Carmen Molina-Parı́s +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #gr-qc
paper · pdf · doi:10.1103/physrevd.59.044011
published as Phys.Rev. D59 (1999) 044011 · 8 pages, ReV-TeX 3.1
arxiv created 1998/10/08 · openalex publication_date 1999/01/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define the bounce in terms of a 3-dimensional edgeless achronal spacelike hypersurface of minimal volume (zero trace for the extrinsic curvature plus a ``flare-out'' condition). This enables us to severely constrain the geometry of spacetime at and near the bounce and to derive general theorems regarding violations of the energy conditions---theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the highly symmetric FRW-based subclass of Tolman wormholes. [For example, even under the mildest of hypotheses, the strong energy condition (SEC) must be violated.] Alternatively, one can dispense with the minimal volume condition and define a generic bounce entirely in terms of the motion of test particles (future-pointing timelike geodesics), by looking at the expansion of their timelike geodesic congruences. One re-confirms that the SEC must be violated at or near the bounce. In contrast, it is easy to arrange for all the other standard energy conditions to be satisfied.