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

TL;DR

This paper analytically investigates large-mass scalar fields non-minimally coupled to Gauss-Bonnet black holes, deriving a formula for the threshold of scalarization in the high-mass regime.

Contribution

It provides a new analytical formula for the critical coupling parameter separating hairy black holes from bare Schwarzschild black holes in the large-mass limit.

Findings

Derived a compact analytical expression for the critical existence line.

Explored properties of scalarized black-hole configurations in the large-mass regime.

Identified the threshold for spontaneous scalarization in the eikonal limit.

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 $\mu r_{\text{H}}\gg1$ 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.