Hairy black holes: stability under odd-parity perturbations and existence of slowly rotating solutions

Abstract

We show that, independently of the scalar field potential and of specific asymptotic properties of the spacetime (asymptotically flat, de Sitter or anti-de Sitter), any static, spherically symmetric or planar, black hole or soliton solution of the Einstein theory minimally coupled to a real scalar field with a general potential is mode stable under linear odd-parity perturbations. To this end, we generalize the Regge-Wheeler equation for a generic self-interacting scalar field, and show that the potential of the relevant Schrödinger operator can be mapped, by the so-called S-deformation, to a semi-positively defined potential. With these results at hand we study the existence of slowly rotating configurations. The frame dragging effect is compared with the Kerr black hole.

11 pages, 1 figure

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• Nonminimal derivative coupling scalar-tensor theories: odd-parity perturbations and black hole stability
• Black hole stability under odd-parity perturbations in Horndeski gravity
• Asymptotically flat black holes with scalar hair: a review
• Odd-parity stability of hairy black holes in $U(1)$ gauge-invariant scalar-vector-tensor theories
• Hairy Black Hole Stability in AdS, Quantum Mechanics on the Half-Line and Holography
• Exact black-hole formation with a conformally coupled scalar field in three dimensions
• Aspects of Stability of Hairy Black Holes