https://doi.org/10.1140/epjc/s10052-019-7494-9
Regular Article - Theoretical Physics
Gauss–Bonnet black holes supporting massive scalar field configurations: the large-mass regime
1
The Ruppin Academic Center, 40250, Emeq Hefer, Israel
2
The Hadassah Academic College, 91010, Jerusalem, Israel
* e-mail: shaharhod@gmail.com
Received:
4
November
2019
Accepted:
18
November
2019
Published online:
25
November
2019
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 
which, for a given mass of the supported scalar field, marks the threshold for the onset of the spontaneous scalarization phenomenon [here 
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 
of large field masses. In particular, we derive a remarkably compact analytical formula for the critical existence-line of the system which separates bare Schwarzschild black-hole spacetimes from composed hairy (scalarized) black-hole-field configurations.
© The Author(s), 2019
