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Gravitating Monopole--Antimonopole Chains and Vortex Rings

Burkhard Kleihaus·Jutta Kunz·Yasha Shnir
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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.

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Burkhard Kleihaus, Jutta Kunz, Yasha Shnir. 2004-11-22. Gravitating Monopole--Antimonopole Chains and Vortex Rings. https://doi.org/10.1103/physrevd.71.024013

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