Spontaneous scalarization of Gauss-Bonnet black holes: Analytic treatment in the linearized regime

Shahar Hod

doi:10.1103/PhysRevD.100.064039

paper

Spontaneous scalarization of Gauss-Bonnet black holes: Analytic treatment in the linearized regime

arXiv:1912.07630 · doi:10.1103/PhysRevD.100.064039

Abstract

It has recently been proved that nontrivial couplings between scalar fields and the Gauss-Bonnet invariant of a curved spacetime may allow a central black hole to support spatially regular scalar hairy configurations. Interestingly, former numerical studies of the intriguing black-hole spontaneous scalarization phenomenon have demonstrated that the composed hairy black-hole-scalar-field configurations exist if and only if the dimensionless coupling parameter $η ˉ$ of the theory belongs to a discrete set ${[η ˉ_{n}^{-}, η ˉ_{n}^{+}]}_{n = 0}^{n = \infty}$ of scalarization bands. We have examined the numerical data that are available in the physics literature and found that the newly discovered hairy black-hole-linearized-massless-scalar-field configurations are characterized by the asymptotic universal behavior $Δ_{n} \equiv η ˉ_{n + 1}^{+} - η ˉ_{n}^{+} ≃ 2.72$ . Motivated by this intriguing observation, in the present paper we study {\it analytically} the physical and mathematical properties of the spontaneously scalarized Schwarzschild black holes in the linearized (weak-field) regime. In particular, we provide a remarkably compact analytical explanation for the numerically observed universal behavior $Δ_{n} ≃ 2.72$ which characterizes the discrete resonant spectrum ${η ˉ_{n}^{+}}_{n = 0}^{n = \infty}$ of the composed hairy black-hole-linearized-scalar-field configurations.

6 pages

Spontaneous scalarization of Gauss-Bonnet black holes: Analytic treatment in the linearized regime

Abstract

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