Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Authors: Piotr Bizoń and Patryk Mach
Journal: Trans. Amer. Math. Soc. 369 (2017), 2029-2048
MSC (2010): Primary 35Q75
DOI: https://doi.org/10.1090/tran/6807
Published electronically: May 17, 2016
Erratum: Trans. Amer. Math. Soc. 369 (2017), 3013-3013.
Supplementary material: Mathematica notebook demo
MathSciNet review: 3581226
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 35Q75

Retrieve articles in all journals with MSC (2010): 35Q75


Additional Information

Piotr Bizoń
Affiliation: Institute of Physics, Jagiellonian University, Kraków, Poland – and – Max Planck Institute for Gravitational Physics (A. Einstein Institute), Golm, Germany
Email: piotr.bizon@aei.mpg.de

Patryk Mach
Affiliation: Institute of Physics, Jagiellonian University, Kraków, Poland
Email: patryk.mach@uj.edu.pl

DOI: https://doi.org/10.1090/tran/6807
Received by editor(s): March 17, 2015
Published electronically: May 17, 2016
Article copyright: © Copyright 2016 American Mathematical Society

American Mathematical Society