# Spontaneous Symmetry Breaking in Wormholes Spacetimes with Matter

## TL;DR

This paper investigates how adding bosonic matter to Ellis wormholes induces spontaneous symmetry breaking, leading to asymmetric solutions that are energetically favored and cause transitions between single and double throat geometries.

## Contribution

It demonstrates the occurrence of spontaneous symmetry breaking in wormhole spacetimes with matter and explores the resulting asymmetric solutions and throat transitions.

## Key findings

- Asymmetric solutions emerge from symmetric ones at bifurcation points.
- Asymmetric solutions are energetically preferred over symmetric ones.
- Transitions between single and double throat configurations occur in the solution space.

## Abstract

When bosonic matter in the form of a complex scalar field is added to Ellis wormholes, the phenomenon of spontaneous symmetry breaking is observed. Symmetric solutions possess full reflection symmetry with respect to the radial coordinate of the two asymptotically flat spacetime regions connected by the wormhole, whereas asymmetric solutions do not possess this symmetry. Depending on the size of the throat, at bifurcation points pairs of asymmetric solutions arise from or merge with the symmetric solutions. These asymmetric solutions are energetically favoured. When the backreaction of the boson field is taken into account, this phenomenon is retained. Moreover, in a certain region of the solution space both symmetric and asymmetric solutions exhibit a transition from single throat to double throat configurations.