Stationary generalizations for the Bronnikov-Ellis wormhole and for the vacuum ring wormhole

Abstract

We analyze possibilities to obtain a globally regular stationary generalization for the ultrastatic wormhole with a repulsive scalar field found by Bronnikov and by Ellis in 1973. The extreme simplicity of this static solution suggests that its stationary version could be obtainable analytically and should be globally regular, but no such generalization has been found. We analyze the problem and find that the difficulty originates in the vacuum theory, since the scalar field can be eliminated within the Eris-Gurses procedure. The problem then reduces to constructing the spinning generalization for the vacuum wormhole sourced by a thin ring of negative tension. Solving the vacuum Ernst equations determines the $g_{00}$, $g_{0\phi }$ metric components and hence the AMD mass $\mathrm{M}$ and angular momentum $\mathrm{J}$, all of these being specified by the ring source. The scalar field can be included into consideration afterwords, but this only affects $g_{rr}$ and $g_{\vartheta \vartheta }$ without changing the rest. Within this approach, we analyze a number of exact stationary generalizations for the wormhole, but none of them are satisfactory. However, the perturbative expansion around the static vacuum background contains only bounded functions and presumably converges to an exact solution. Including the scalar field screens the singularity at the ring source and renders the geometry regular. This solution describes a globally regular spinning wormhole with two asymptotically flat regions. Even though the source itself is screened and not visible, the memory of it remains in $g_{00}$ and $g_{0\phi }$ and accounts for the $\mathrm{M}\propto {\mathrm{J}}^2$ relation typical for a rotating extended source. Describing stationary spacetimes with an extended source is a complicated problem, which presumably explains the difficulty in finding the solution.

arXiv comment37 pages, references added, minor style improvements

References in corpus (26)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Wormholes in Dilatonic Einstein-Gauss-Bonnet Theory
• The null energy condition in dynamic wormholes
• Possible wormholes in a brane world
• Rotating traversable wormholes
• Fate of the first traversible wormhole: black-hole collapse or inflationary expansion
• Topological Censorship
• Rehabilitating space-times with NUTs
• Rotating Ellis Wormholes in Four Dimensions
• NUT wormholes
• Geometry of Spinning Ellis Wormholes
• Slowly rotating scalar field wormholes: the second order approximation
• No stable wormholes in Einstein-dilaton-Gauss-Bonnet theory
• Weyl metrics and wormholes
• Quasi-periodic oscillations from the accretion disk around rotating traversable wormholes
• From Schwarzschild to Kerr: Generating spinning Einstein-maxwell fields from static fields
• Zero mass limit of Kerr spacetime is a wormhole
• Scalar wormholes with nonminimal derivative coupling
• Generation of rotating solutions in Einstein-scalar gravity
• Ring wormholes via duality rotations
• Uniqueness theorem for static wormholes in Einstein-phantom scalar field theory
• Class of Einstein-Maxwell Phantom Fields: Rotating and Magnetised Wormholes
• Giant wormholes in ghost-free bigravity theory
• Axisymmetric multiwormholes revisited
• Scalar multi-wormholes

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• Radial perturbations of Ellis-Bronnikov wormholes in slow rotation up to second order
• Multi-Sheet Wormholes in the Gravitational Soliton Formalism
• Dynamical Formation of Charged Wormholes
• Quadrupole perturbations of slowly spinning Ellis-Bronnikov wormholes
• Uniqueness of electrically and magnetically charged phantom wormholes