You Can't Get Through Szekeres Wormholes - or - Regularity, Topology and Causality in Quasi-Spherical Szekeres Models

Details You Can't Get Through Szekeres Wormholes - or - Regularity, Topology and Causality in Quasi-Spherical Szekeres Models You Can't Get Through Szekeres Wormholes - or - Regularity, Topology and Causality in Quasi-Spherical Szekeres Models

2002-06-18

arxiv.org/abs/gr-qc/0206052v4

Phys.Rev.D66:084011,2002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

zip file with LaTeX text + 6 figures (.eps & .ps). 47 pages. Second replacement corrects some minor errors and typos. (First r

Scientific paper

10.1103/PhysRevD.66.084011

The spherically symmetric dust model of Lemaitre-Tolman can describe wormholes, but the causal communication between the two asymptotic regions through the neck is even less than in the vacuum (Schwarzschild-Kruskal-Szekeres) case. We investigate the anisotropic generalisation of the wormhole topology in the Szekeres model. The function E(r, p, q) describes the deviation from spherical symmetry if \partial_r E \neq 0, but this requires the mass to be increasing with radius, \partial_r M > 0, i.e. non-zero density. We investigate the geometrical relations between the mass dipole and the locii of apparent horizon and of shell-crossings. We present the various conditions that ensure physically reasonable quasi-spherical models, including a regular origin, regular maxima and minima in the spatial sections, and the absence of shell-crossings. We show that physically reasonable values of \partial_r E \neq 0 cannot compensate for the effects of \partial_r M > 0 in any direction, so that communication through the neck is still worse than the vacuum. We also show that a handle topology cannot be created by identifying hypersufaces in the two asymptotic regions on either side of a wormhole, unless a surface layer is allowed at the junction. This impossibility includes the Schwarzschild-Kruskal-Szekeres case.

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