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Non-Abelian clouds around Reissner-Nordström black holes: The existence line

Eugen Radu1, D. H. Tchrakian2,3, and Yisong Yang4

  • 1Departamento de Fisica da Universidade de Aveiro and CIDMA, Campus de Santiago, 3810-183 Aveiro, Portugal
  • 2School of Theoretical Physics—DIAS, 10 Burlington Road, Dublin 4, Ireland
  • 3Department of Computer Science, National University of Ireland Maynooth, Maynooth, Ireland
  • 4Department of Mathematics, Tandon School, New York University, Brooklyn, New York 11201, USA

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Phys. Rev. D 93, 124069 – Published 27 June, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.124069

Abstract

A known feature of electrically charged Reissner–Nordström–anti-de Sitter planar black holes is that they can become unstable when considered as solutions of Einstein-Yang-Mills theory. The mechanism for this is that the linearized Yang-Mills equations in the background of the Reissner-Nordström (RN) black holes possess a normalizable zero mode, resulting in non-Abelian (nA) magnetic clouds near the horizon. In this work we show that the same pattern may occur also for asymptotically flat RN black holes. Different from the anti–de Sitter case, in the Minkowskian background the prerequisites for the existence of the nA clouds are (i) a large enough gauge group, and (ii) the presence of some extra interaction terms in the matter Lagrangian. To illustrate this mechanism we present two specific examples, one in four- and the other in five-dimensional asymptotically flat spacetime. In the first case, we augment the usual SU(3) Yang-Mills Lagrangian with a higher-order (quartic) curvature term, while for the second one we add the Chern-Simons density to the SO(6) Yang-Mills system. In both cases, an Abelian gauge symmetry is spontaneously broken near a RN black hole horizon with the appearance of a condensate of nA gauge fields. In addition to these two examples, we review the corresponding picture for anti–de Sitter black holes. All these solutions are studied both analytically and numerically, existence proofs being provided for nA clouds in the background of RN black holes. The proofs use shooting techniques which are suggested by and in turn offer insights for our numerical methods. They indicate that, for a black hole of given mass, appropriate electric charge values are required to ensure the existence of solutions interpolating desired boundary behavior at the horizons and spatial infinity.

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Phys. Rev. D 93, 124069– Published 27 June, 2016
  • Received 19 April 2016

© 2016 American Physical Society

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