Ring wormholes via duality rotations

TL;DR

This paper constructs novel ring-shaped wormhole geometries by applying duality transformations to known metrics, revealing configurations with negative tension rings that connect two flat universes and could be formed by negative energy distributions.

Contribution

It introduces a new class of vacuum ring wormholes derived from duality rotations, expanding the understanding of possible wormhole geometries without scalar fields.

Findings

Ring wormholes have a ring encircling the throat with adjustable radius.

Tension of the ring is always negative and less than a specific bound.

At maximal tension, the geometry is flat but retains non-trivial topology.

Abstract

We apply duality rotations and complex transformations to the Schwarzschild metric to obtain wormhole geometries with two asymptotically flat regions connected by a throat. In the simplest case these are the well-known wormholes supported by phantom scalar field. Further duality rotations remove the scalar field to yield less well known vacuum metrics of the oblate Zipoy-Voorhees-Weyl class, which describe ring wormholes. The ring encircles the wormhole throat and can have any radius, whereas its tension is always negative and should be less than $-c^4/4G$. If the tension reaches the maximal value, the geometry becomes exactly flat, but the topology remains non-trivial and corresponds to two copies of Minkowski space glued together along the disk encircled by the ring. The geodesics are straight lines, and those which traverse the ring get to the other universe. The ring therefore literally produces a hole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes, for example by vacuum fluctuations.