A Yang-Mills field on the extremal Reissner-Nordström black hole

Abstract

We consider a spherically symmetric (magnetic) $SU(2)$ Yang-Mills field propagating on the exterior of the extremal Reissner-Nordström black hole. Taking advantage of the conformal symmetry, we reduce the problem to the study of the Yang-Mills equation in a geodesically complete spacetime with two asymptotically flat ends. We prove the existence of infinitely many static solutions (two of which are found in closed form) and determine the spectrum of their linear perturbations and quasinormal modes. Finally, using the hyperboloidal approach to the initial value problem, we describe the process of relaxation to the static endstates of evolution for various initial data.

arXiv comment15 pages, 7 figures

References in corpus (7)

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• Hyperboloidal foliations and scri-fixing
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• Solving systems of transcendental equations involving the Heun functions
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Cited by in corpus (7)

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• Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system
• Asymptotic blow-up for a class of semilinear wave equations on extremal Reissner-Nordström spacetimes
• Late-time decay of coupled electromagnetic and gravitational perturbations outside an extremal charged black hole
• Are gravitating magnetic monopoles stable?
• Horizon Hair from Inversion Symmetry
• Yang--Mills Monopoles in Extremal Reissner--Nordström Black Hole Metric