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

Bizon, Piotr; Kahl, Michał

doi:10.1088/0264-9381/33/17/175013

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

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Bizon, Piotr
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Bizon, P., & Kahl, M. (2016). A Yang-Mills field on the extremal Reissner-Nordström black hole. Classical and quantum gravity, 33(17): 175013. doi:10.1088/0264-9381/33/17/175013.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-87D8-6

Abstract

We consider a spherically symmetric (magnetic) $SU(2)$ Yang-Mills field propagating on the exterior of the extremal Reissner-Nordstr\"om 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.