Wormhole $C$ metric

TL;DR

This paper introduces a new family of exact AdS wormhole solutions supported by phantom scalar fields, generalizing the C-metric, with fully resolved conical singularities and detailed causal structure analysis.

Contribution

It presents novel exact solutions for accelerated wormholes in AdS with a scalar potential derived from supergravity, extending previous C-metric models.

Findings

Resolved conical singularities in the wormhole solutions.

Existence of two branches of static AdS wormholes.

Detailed analysis of the global causal structure.

Abstract

The C-metric in vacuum general relativity describes a pair of accelerated black holes supported by conical singularity. In this paper, we present a new family of exact solutions to the Einstein-phantom scalar system that describes accelerated wormholes in AdS. In the zero acceleration limit with a vanishing potential, the present solution recovers the asymptotically flat wormhole originally constructed by Ellis and Bronnikov. The scalar potential of the phantom field has an infinite number of critical points and is expressed in terms of the superpotential, which is obtained by suitable analytic continuation of one parameter family of the ${\cal N}=2$ gauged supergravity. As one traverses two asymptotic regions connected by throat, the scalar field evolves from AdS, corresponding to the origin of the potential, towards the neighboring AdS local minimum of the potential. We find that the flipping transformation, which interchanges the role of ``radial'' and "angular'' coordinates at the expense of double Wick rotation, is an immediate cause for the existence of two branches of static AdS wormholes discovered previously. Contrary to the ordinary C-metric, the conical singularity along the symmetry axis can be completely resolved, when the (super)potential is periodic or zero. We explore the global causal structure in detail.