A Yang–Mills field on the extremal Reissner–Nordström black hole. (15th August 2016)

• Record Type: Journal Article
• Authors: Bizoń, Piotr; Kahl, Michał
• Is Part Of: Classical and quantum gravity. Volume 33:Number 17(2016:Sep.)
• Publication Date: 2016-08-15
• Subjects: Yang–Mills -- Reissner–Nordström -- hyperboloidal foliations; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/33/17/175013
• Languages: English
• ISSNs: 0264-9381

Abstract

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, both stable (for generic initial data) and unstable (for codimension-one initial data).