Weyl metrics and wormholes

Abstract

We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing conical singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts along the symmetry axes, apart from solutions with locally flat geometry.

42 pages, 9 figures, added references and an appendix discussing the Flamm embedding versus Einstein-Rosen bridge; matches the published version

References in corpus (6)

• Traversable wormholes: Some simple examples
• The non-integrability of the Zipoy-Voorhees metric
• Ring wormholes via duality rotations
• Giant wormholes in ghost-free bigravity theory
• Super-Geometrodynamics
• Static axisymmetric rings in general relativity: How diverse they are

Cited by in corpus (28)

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• Spinning test particle motion around a traversable wormhole
• Zero mass limit of Kerr spacetime is a wormhole
• Axially symmetric and static solutions of Einstein equations with self-gravitating scalar field
• Static spacetimes haunted by a phantom scalar field: classification and global structure in the massless case
• Generation of rotating solutions in Einstein-scalar gravity
• Particle motion around a static axially symmetric wormhole
• Uniqueness theorem for static wormholes in Einstein-phantom scalar field theory
• Static spacetimes haunted by a phantom scalar field III: asymptotically (A)dS solutions
• Generalized Ellis-Bronnikov graphene wormhole
• Static spacetimes haunted by a phantom scalar field II: dilatonic charged solutions
• Stationary generalizations for the Bronnikov-Ellis wormhole and for the vacuum ring wormhole
• Uniqueness theorem for static phantom wormholes in Einstein-Maxwell-dilaton theory
• High energy particle collisions in static, spherically symmetric black-hole-like wormholes
• Uniqueness of higher-dimensional Einstein-Maxwell-phantom dilaton wormholes
• A Maximum Force Perspective on Black Hole Thermodynamics, Quantum Pressure, and Near-Extremality
• Static axionlike dark matter clouds around magnetized rotating wormholes -- probe limit case
• Ring wormholes and time machines
• Simple traversable wormholes violating energy conditions only near the Planck scale
• Classification of static black holes in Einstein phantom/dilaton Maxwell/anti-Maxwell gravity systems
• Exact solution of the wave equation of a scalar particle in the zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times
• Higher-dimensional Buchdahl and Janis-Robinson-Winicour transformations in the Einstein-Maxwell system with a massless scalar field
• Self-collision of a portal wormhole
• A quadrupolar generalization of the Erez-Rosen coordinates
• Uniqueness of electrically and magnetically charged phantom wormholes
• Zero Mass limit of Kerr-MOG Black Hole Equals Wormhole
• Interacting Kerr-Newman Electromagnetic Fields
• Phantom scalar field counterpart to Curzon-Chazy spacetime