Initial Data Problem for a Traversable Wormhole with Interacting Mouths

Abstract

We consider the time-symmetric initial data problem for GR minimally coupled to a phantom scalar field and a Maxwell field. The main focus is on initial data sets describing two interacting mouths of the same traversable wormhole. These data sets are similar in many respects to the Misner initial data with two black holes. More precisely, the corresponding solutions of the constraint equations determine the initial geometries which are topologically equivalent to the manifold \(\mathbb{S}^{2}\times\mathbb{S}^{1}\)-{point} (i.e., \({\mathbb{R}^{3}}\) with a “handle”) and therefore describe initial states of intra-universe wormholes. Thus the results of the paper can be considered as an input for numerical simulation of such wormholes.