Gauss\u2013Bonnet black holes supporting massive scalar field configurations: the large-mass regime

Shahar Hod

doi:10.1140/epjc/s10052-019-7494-9

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.

Highlights

The mathematically elegant no-hair theorems presented in [1,2,3,4] have revealed the physically important fact that, within the framework of classical general relativity, spherically symmetric black holes with regular horizons cannot support external static matter configurations which are made of scalar fields with minimal coupling to gravity
Later developments [8,9,10,11,12,13,14] have revealed the intriguing fact that spatially regular hairy matter configurations which are made of scalar fields with non-minimal couplings to the Gauss-Bonnet curvature invariant G may be supported in curved black-hole spacetimes
The recently published highly interesting works [12,13,14,19] have explicitly proved that, in some field theories, black holes may support external matter configurations made of scalar fields, a phenomenon which is known by the name black-hole spontaneous scalarization

Summary

Introduction

The mathematically elegant no-hair theorems presented in [1,2,3,4] have revealed the physically important fact that, within the framework of classical general relativity, spherically symmetric black holes with regular horizons cannot support external static matter configurations which are made of scalar fields with minimal coupling to gravity. Later developments [8,9,10,11,12,13,14] have revealed the intriguing fact that spatially regular hairy matter configurations which are made of scalar fields with non-minimal couplings to the Gauss-Bonnet curvature invariant G may be supported in curved black-hole spacetimes. The physical parameter α is the dimensionless coupling constant of the non-trivial field theory [see Eq (10) below]

Objectives

Conclusion