Axisymmetric multiwormholes revisited

TL;DR

This paper reviews the construction of axisymmetric multiwormhole solutions in gravitating theories, highlighting the inevitability of strut singularities and the complex topology of their extended solutions.

Contribution

It provides a comprehensive review of multiwormhole solutions, including their analytical continuation and topological properties, revealing limitations in achieving asymptotic flatness.

Findings

Strut singularities are unavoidable except in special cases.

Extended solutions have complex multi-sheeted topologies.

Maximally extended solutions cannot be asymptotically flat in all sheets.

Abstract

The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the $n$ cuts associated with the wormhole mouths. The resulting Riemann manifold has $2^n$ sheets interconnected by $2^{n-1}n$ wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.