Superradiant instability of extremal brane-world Reissner-Nordstr\"{o}m black holes to charged scalar perturbations

TL;DR

This paper investigates the stability of extremal braneworld Reissner-Nordström black holes under charged scalar perturbations, revealing that higher dimensions can induce a superradiant instability due to a trapping potential well.

Contribution

It demonstrates that extra dimensions create a trapping potential well outside extremal braneworld black holes, leading to superradiant instability, a phenomenon absent in four-dimensional cases.

Findings

Superradiant amplification occurs in braneworld charged black holes.

A trapping potential well appears only in higher-dimensional spacetimes.

Higher dimensions induce superradiant instability in extremal braneworld black holes.

Abstract

We examine the stability of extremal braneworld Reissner-Nordstr\"{o}m black holes under massive charged scalar perturbations. We show that similar to the four-dimensional case, the superradiant amplification can occur in braneworld charged holes. More interestingly we find that when the spacetime dimension is higher than four, a trapping potential well can emerge outside the braneworld black hole. This potential well is the extra dimensional effect and does not exist in four dimensions. It triggers the superradiant instability of the extremal braneworld charged holes.