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

TL;DR

This paper analyzes the limitations of Szekeres wormholes, showing that anisotropy cannot improve causal communication between regions and that creating a handle topology requires a surface layer, even in vacuum cases.

Contribution

It demonstrates that anisotropic Szekeres models cannot facilitate better causal communication in wormholes and that handle topologies require surface layers at junctions.

Findings

Causal communication through Szekeres wormholes is worse than in vacuum cases.

Anisotropy cannot compensate for increasing mass with radius in wormhole models.

Handle topologies cannot be formed without a surface layer at the junction.

Abstract

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.