Gauss-Bonnet black holes supporting massive scalar field configurations: The large-mass regime

Abstract

It has recently been demonstrated that black holes with spatially regular horizons can support external scalar fields (scalar hairy configurations) which are non-minimally coupled to the Gauss-Bonnet invariant of the curved spacetime. The composed black-hole-scalar-field system is characterized by a critical existence line $\alpha =\alpha (\mu r_{\text{H}})$ which, for a given mass of the supported scalar field, marks the threshold for the onset of the spontaneous scalarization phenomenon [here $\{\alpha ,\mu ,r_{\text{H}}\}$ are respectively the dimensionless non-minimal coupling parameter of the field theory, the proper mass of the scalar field, and the horizon radius of the central supporting black hole]. In the present paper we use analytical techniques in order to explore the physical and mathematical properties of the marginally-stable composed black-hole-linearized-scalar-field configurations in the eikonal regime $\mu r_{\text{H}}\gg 1$ of large field masses. In particular, we derive a remarkably compact analytical formula for the critical existence-line $\alpha =\alpha (\mu r_{\text{H}})$ of the system which separates bare Schwarzschild black-hole spacetimes from composed hairy (scalarized) black-hole-field configurations.

5 pages

References in corpus (5)

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Cited by in corpus (8)

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• Shrouded black holes in Einstein-Gauss-Bonnet gravity
• Dynamics of scalar hair with self-interactions around a Schwarzchild black hole
• Charged Gauss-Bonnet black holes supporting non-minimally coupled scalar clouds: Analytic treatment in the near-critical regime
• Non-equatorial scalar rings supported by magnetized Schwarzschild-Melvin black holes
• Higher dimensional Reissner-Nordström black holes supporting static scalar shells