Abstract
We describe the construction of traversable wormholes with multiple mouths in four spacetime dimensions and discuss associated quantum entanglement. Our wormholes may be traversed between any pair of mouths. In particular, in the three-mouth case they have fundamental group F2 (the free group on two generators). By contrast, connecting three regions A, B, C in pairs (AB, BC, and AC) using three separate wormholes would give fundamental group F3. Our solutions are asymptotically flat up to the presence of possible magnetic fluxes or cosmic strings that extend to infinity. The construction begins with a two-mouth traversable wormhole supported by backreaction from quantum fields. Inserting a sufficiently small black hole into its throat preserves traversability between the original two mouths. This black hole is taken to be the mouth of another wormhole connecting the original throat to a new distant region of spacetime. Making the new wormhole traversable in a manner similar to the original two-mouth wormhole provides the desired causal connections. From a dual field theory point of view, when AdS asymptotics are added to our construction, multiparty entanglement may play an important role in the traversability of the resulting wormhole.
Highlights
A single mouth in each region, as backgrounds with more interesting connectivity require some sort of finite causal shadow, and this in turn necessitates a larger amount of negative energy to make the wormhole traversable
Our analysis begins with the more familiar two-mouth asymptotically flat wormholes of [5], enhanced by including a large number Nf of four-dimensional massless fermions. We perturb this solution by adding a small black hole to the bottom of the wormhole throat
We presented a construction of a multi-mouth traversable wormhole. This was done by starting with a two-mouth traversable wormhole of the form described in [5]. We perturbed this solution by adding a small black hole in the throat of the larger wormhole
Summary
We review here the construction of two-mouth traversable wormholes in four-dimensional asymptotically flat space of [5]. To make a traversable wormhole that connects different portions of asymptotically flat space, the metric must be modified to allow the size of the S2 to vary, so that the black hole spacetime can be sewn onto the asymptotically flat region One may take this variation to be slow, with the perturbation away from AdS2 × S2 being of the form. We emphasize that the magnetic field lines must form closed loops in order to generate Casimir energy This requires that both wormhole mouths be placed in the same asymptotic region of spacetime. Additional structure can be added to create longer-lived traversable wormhole solutions This can be achieved by introducing an external magnetic field (in GR, this would be a Melvin flux tube [13]) tuned to keep the mouths apart, or by attaching cosmic strings that pull them (exact solutions exist for both mechanisms [14, 15]). These statements prohibit wormholes from being the fastest causal curves between distant points, and the travel time through wormholes of [5] is longer by a factor of order unity.
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