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 = 21/5\documentclass[12pt]{minimal}
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\begin{document}$$ \sqrt{21}/5 $$\end{document} 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 ηQ/MMμnn=0n=∞\documentclass[12pt]{minimal}
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\begin{document}$$ {\left\{\eta \left(Q/M, M\mu; n\right)\right\}}_{n=0}^{n=\infty } $$\end{document} 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.
