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.