Higher dimensional Reissner-Nordström black holes supporting static scalar shells

We analytically study scalarization of higher-dimensional charged Reissner-Nordström (RN) black hole. It is shown that static massive scalar field which is non-minimally coupled to Gauss-Bonnet invariant can be supported by higher-dimensional black hole in super-critical charge regime Q/M≥C¯d with Q,M charge and mass of the black hole and C¯d some unitless spacetime dimension-dependent quantity. Moreover, we show that the static massive scalar shell can be quite thin in the large mass regime μM1d−3≫1 with μ mass of the scalar field.