Traversable Wormholes with Spontaneous Symmetry Breaking

Abstract

We argue that a spherically symmetric traversable wormhole solution of the Einstein field equations can be supported by minimally coupled self-interacting scalar field which allows a spontaneous symmetry breaking of the field around the wormhole throat. We study two cases : (i) the phantom wormhole solution of Bronnikov and (ii) a generalized Kiselev wormhole. We study the property of radial null geodesics and show that the metric can describe either a two-way or a one-way traversable wormhole depending on certain parameter ranges. The scalar field exhibits spontaneous symmetry breaking within the coordinate range where a wormhole throat forms and helps one suggest that spontaneous symmetry breaking may act as a threshold for wormhole throat formation. We also compute the radius of the photon sphere, the Lyapunov exponent, the shadow radius, and the innermost stable circular orbits for the geometries.

26 pages, 19 figures, abstract changed, New section and references added, comments are welcome