Growing Hair on the extremal $BTZ$ black hole

Abstract

We show that the nonlinear $\sigma -$model in an asymptotically $Ad{S}_3$ space-time admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear $\sigma -$model fields and minimally coupled to gravity. The local symmetry transformation simultaneously twists the nonlinear $\sigma -$model fields and changes the space-time metric, and it can be used to map an extremal $BTZ$ black hole to infinitely many hairy black hole solutions.

11 pages, 1 figure, minor corrections included

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Cited by in corpus (5)

• Stationary scalar clouds around a BTZ black hole
• Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields
• A New Paradigm for Topological or Rotational Non-Abelian Gauge Fields from Einstein-Skyrme Holography
• Exactly solvable gravitating perfect fluid solitons in (2+1) dimensions
• Rotating AdS Einstein universes from constrained metrics