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Gravitating Monopole--Antimonopole Chains and Vortex Rings
General Relativity and Quantum Cosmology · Submitted 22 Nov 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We construct monopole-antimonopole chain and vortex solutions in Yang-Mills-Higgs theory coupled to Einstein gravity.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We construct monopole-antimonopole chain and vortex solutions in Yang-Mills-Higgs theory coupled to Einstein gravity. | contribution 1.00 | 0.96 | 0.16 | asserted 1.00 |
| s1 | The solutions are static, axially symmetric and asymptotically flat. | result 0.91 | 0.81 | 0.04 | asserted 1.00 |
| s2 | They are characterized by two integers (m,n) where m is related to the polar angle and n to the azimuthal angle. | result 0.74 | 0.73 | 0.05 | asserted 1.00 |
| s3 | Solutions with n=1 and n=2 correspond to chains of m monopoles and antimonopoles. | result 0.84 | 0.80 | 0.07 | asserted 1.00 |
| s4 | Here the Higgs field vanishes at m isolated points along the symmetry axis. | result 0.98 | 0.76 | 0.04 | asserted 1.00 |
| s5 | Larger values of n give rise to vortex solutions, where the Higgs field vanishes on one or more rings, centered around the symmetry axis. | result 0.88 | 0.84 | 0.09 | asserted 1.00 |
| s6 | 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. | result 0.91 | 0.88 | 0.37 | asserted 1.00 |
| s7 | This upper branch has no flat space limit. | result 0.99 | 0.84 | 0.08 | asserted 1.00 |
| s8 | 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. | result 0.99 | 0.80 | 0.15 | asserted 0.84 |
| s9 | In this latter case further branches of solutions appear. | result 0.99 | 0.82 | 0.05 | asserted 1.00 |
| s10 | 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. | result 0.55 | 0.85 | 0.12 | asserted 1.00 |
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Original 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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3 arXiv papers cite this in 3 sentences
Papers citing it · 1 sentence without a confident label
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Note that there is a difference between the evolutions of the configurations we are considering here in this $4+1$ dimensional theory, and the behaviour of the gravitating multimonopoles or the monopole-antimonopole solutions of the gravitating YMH system $3+1$ theory [ref] .
d=4+1 gravitating nonabelian solutions with bi-azimuthal symmetry · $n=1$ · 1.00
Cites it as background 1 paper
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Similar chain-like configurations are also present in flat space-time analogs of BSs, known as Q-balls [ref] , and have been extensively studied in other soliton models such as Skyrmions [ref] , sphalerons [ref] and dyons [ref] .
Bifurcations in Bosonic Stars: chains and rings from spherical solutions · Introduction · 0.88
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