Ring wormholes via duality rotations

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.

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References in corpus (16)

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• Cool horizons for entangled black holes
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• The quantum inequalities do not forbid spacetime shortcuts
• Scalar wormholes with nonminimal derivative coupling
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Cited by in corpus (20)

• Weyl metrics and wormholes
• Zero mass limit of Kerr spacetime is a wormhole
• Generation of rotating solutions in Einstein-scalar gravity
• Uniqueness theorem for static wormholes in Einstein-phantom scalar field theory
• Stationary generalizations for the Bronnikov-Ellis wormhole and for the vacuum ring wormhole
• Static axisymmetric rings in general relativity: How diverse they are
• Uniqueness theorem for static phantom wormholes in Einstein-Maxwell-dilaton theory
• Uniqueness of higher-dimensional Einstein-Maxwell-phantom dilaton wormholes
• A Maximum Force Perspective on Black Hole Thermodynamics, Quantum Pressure, and Near-Extremality
• Classification of static black holes in Einstein phantom/dilaton Maxwell/anti-Maxwell gravity systems
• Ring wormholes and time machines
• Static axionlike dark matter clouds around magnetized rotating wormholes -- probe limit case
• Simple traversable wormholes violating energy conditions only near the Planck scale
• Exact solution of the wave equation of a scalar particle in the zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times
• The Hookean Law of Black Holes and Fragmentation: Insights from Maximum Force Conjecture and Ruppeiner Geometry
• Self-collision of a portal wormhole
• Geodesic completeness of a ring wormhole
• Interacting Kerr-Newman Electromagnetic Fields
• Zero Mass limit of Kerr-MOG Black Hole Equals Wormhole
• Uniqueness of electrically and magnetically charged phantom wormholes