Higher dimensional Reissner-Nordstr\"{o}m black holes supporting static scalar shells

TL;DR

This paper analytically investigates how higher-dimensional charged Reissner-Nordström black holes can support static scalar fields non-minimally coupled to the Gauss-Bonnet invariant, revealing conditions for scalarization and properties of scalar shells.

Contribution

It provides the first analytical demonstration of scalarization of higher-dimensional RN black holes supported by static scalar shells with non-minimal coupling.

Findings

Scalar fields can be supported in super-critical charge regimes.

Scalar shells can be very thin in the large mass limit.

Scalarization depends on the spacetime dimension and charge-to-mass ratio.

Abstract

We analytically study scalarization of higher-dimensional charged Reissner-Nordstr\"{o}m (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 $Q/M\ge \bar{C}_d$ with $Q, M$ charge and mass of the black hole and $\bar{C}_d$ some unitless spacetime dimension-dependent quantity. Moreover, we show that the static massive scalar shell can be quite thin in the large mass regime $\mu M^{\frac{1}{d-3}}\gg 1$ with $\mu$ mass of the scalar field.