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.

37 pages, references added, minor style improvements

References in corpus (8)

• Rotating Ellis Wormholes in Four Dimensions
• Geometry of Spinning Ellis Wormholes
• Slowly rotating scalar field wormholes: the second order approximation
• Quasi-periodic oscillations from the accretion disk around rotating traversable wormholes
• Zero mass limit of Kerr spacetime is a wormhole
• Ring wormholes via duality rotations
• Uniqueness theorem for static wormholes in Einstein-phantom scalar field theory
• Giant wormholes in ghost-free bigravity theory

Cited by in corpus (9)

• Rotating traversable wormholes in Einstein-Maxwell theory
• Quasinormal modes of rapidly rotating Ellis-Bronnikov wormholes
• Newman-Janis algorithm's application to regular black hole models
• Static axionlike dark matter clouds around magnetized rotating wormholes -- probe limit case
• 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