Bubble universes and traversable wormholes

Abstract

Bubble universes and traversable wormholes in general relativity can be realized as two sides of the same concept. To exemplify it, we find, display, and study in a unified manner a Minkowski-Minkowski closed universe and a Minkowski-Minkowski traversable wormhole. By joining two 3-dimensional flat balls along a thin shell two-sphere of matter, i.e., a spherical domain wall, into a single spacetime one gets a Minkowski-Minkowski static closed universe, i.e., a bubble universe. By joining two 3-dimensional complements of flat balls along a thin shell two-sphere of matter, i.e., a spherical throat, into a single spacetime one gets a Minkowski-Minkowski static open universe which is a traversable wormhole. Thus, Minkowski-Minkowski bubble universes and wormholes can be seen as complementary to each other. It is also striking that these two spacetimes, the Minkowski-Minkowski bubble universe and the Minkowski-Minkowski traversable wormhole, have resemblances with two well-known static universes of general relativity. The Minkowski-Minkowski static closed universe, i.e., the Minkowski-Minkowski bubble universe, resembles in many aspects the Einstein universe, i.e., a static closed spherical universe homogeneously filled with dust matter and with a cosmological constant. The Minkowski-Minkowski static open universe, i.e., the Minkowski-Minkowski traversable wormhole, resembles the Friedmann static universe, i.e., a static open hyperbolic universe homogeneously filled with negative energy density dust and with a negative cosmological, which is a universe with two disjoint branes, or branches, and can be considered a failed wormhole. In this light, the Einstein static closed universe and the Friedmann static open universe should also be seen as the two sides of the same concept, i.e., they are complementary to each other. The scheme is completed by performing a linear stability analysis for the Minkowski-Minkowski bubble universe and the Minkowski-Minkowski traversable wormhole and also by comparing it to the stability of the Einstein static universe and the Friedmann static universe, respectively. This complementarity between bubble universes and traversable wormholes, that exists for these instances of static spacetimes, can be carried out for dynamical spacetimes, indicating that such a complementarity is quite general. The overall study suggests that bubble universes and traversable wormholes can be seen as coming out of the same concept, and thus, if one type of solution exists the other should also exist.