Infinitesimally thin static scalar shells surrounding charged Gauss-Bonnet black holes

Abstract

Abstract We reveal the existence of a new form of spontaneously scalarized black-hole configurations. In particular, it is proved that Reissner-Nordström black holes in the highly charged regime Q/M > (Q/M)crit = $$ \sqrt{21}/5 $$ 21 / 5 can support thin matter shells that are made of massive scalar fields with a non-minimal coupling to the Gauss-Bonnet invariant of the curved spacetime. These static scalar shells, which become infinitesimally thin in the dimensionless large-mass Mμ » 1 regime, hover a finite proper distance above the black-hole horizon [here {M, Q} are respectively the mass and electric charge of the central supporting black hole, and μ is the proper mass of the supported scalar field]. In addition, we derive a remarkably compact analytical formula for the discrete resonance spectrum $$ {\left\{\eta \left(Q/M, M\mu; n\right)\right\}}_{n=0}^{n=\infty } $$ η Q / M Mμ n n = 0 n = ∞ of the non-trivial coupling parameter which characterizes the bound-state charged-black-hole-thin-massive-scalar-shell cloudy configurations of the composed Einstein-Maxwell-scalar field theory.