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Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space

Bizon, P., & Mach, P. (2017). Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space. Transactions of the American Mathematical Society, 369(3), 2029-2048. doi:10.1090/tran/6807.

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Genre: Journal Article

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American Mathematical Society
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### Creators

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Creators:
Bizon, Piotr1, Author
Mach, Patryk, Author
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1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, escidoc:24008

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Free keywords: Mathematics, Analysis of PDEs, math.AP,General Relativity and Quantum Cosmology, gr-qc
Abstract: We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius $\alpha$. Static solutions in this model are shown to exhibit an interesting bifurcation pattern in the parameter $\alpha$. We relate this pattern to the Morse index of the static solution with maximal energy. Using a hyperboloidal approach to the initial value problem, we describe the relaxation to the ground state solution for generic initial data and unstable static solutions for initial data of codimension one, two, and three.

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Dates: 2014-10-162017
Publication Status: Published in print
Pages: 23 pages, 11 figures
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Identifiers: arXiv: 1410.4317
URI: http://arxiv.org/abs/1410.4317
DOI: 10.1090/tran/6807
Degree: -

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Title: Transactions of the American Mathematical Society
Source Genre: Journal
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Pages: - Volume / Issue: 369 (3) Sequence Number: - Start / End Page: 2029 - 2048 Identifier: -