Gravitating Monopole--Antimonopole Chains and Vortex Rings

TL;DR

This paper constructs and analyzes gravitating monopole-antimonopole chains and vortex solutions in Einstein-Yang-Mills-Higgs theory, revealing complex solution branches and connections to known solutions like Bartnik-McKinnon configurations.

Contribution

It introduces new gravitating monopole-antimonopole and vortex solutions with detailed characterization and explores their connection to existing Einstein-Yang-Mills solutions.

Findings

Solutions characterized by two integers (m,n) with distinct monopole and vortex configurations.

Existence of solution branches merging at a maximal coupling constant, with some branches connecting to known solutions.

Discovery of new Einstein-Yang-Mills solutions for specific parameter ranges.

Abstract

We construct monopole-antimonopole chain and vortex solutions in Yang-Mills-Higgs theory coupled to Einstein gravity. The solutions are static, axially symmetric and asymptotically flat. They are characterized by two integers (m,n) where m is related to the polar angle and n to the azimuthal angle. Solutions with n=1 and n=2 correspond to chains of m monopoles and antimonopoles. Here the Higgs field vanishes at m isolated points along the symmetry axis. Larger values of n give rise to vortex solutions, where the Higgs field vanishes on one or more rings, centered around the symmetry axis. When gravity is coupled to the flat space solutions, a branch of gravitating monopole-antimonopole chain or vortex solutions arises, and merges at a maximal value of the coupling constant with a second branch of solutions. This upper branch has no flat space limit. Instead in the limit of vanishing coupling constant it either connects to a Bartnik-McKinnon or generalized Bartnik-McKinnon solution, or, for m>4, n>4, it connects to a new Einstein-Yang-Mills solution. In this latter case further branches of solutions appear. For small values of the coupling constant on the upper branches, the solutions correspond to composite systems, consisting of a scaled inner Einstein-Yang-Mills solution and an outer Yang-Mills-Higgs solution.