Superradiant stability of five and six-dimensional extremal Reissner-Nordstrom black holes

TL;DR

This paper proves that five and six-dimensional extremal Reissner-Nordstrom black holes are stable against superradiant instabilities caused by charged massive scalar perturbations, extending previous four-dimensional results.

Contribution

The authors develop a new analytical method based on Descartes' rule of signs to demonstrate superradiant stability in higher-dimensional extremal black holes.

Findings

Effective potential has only one maximum outside the horizon.

No potential well exists for superradiance modes.

Results extend stability proof to higher dimensions.

Abstract

The superradiant stability of five and six-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation is studied. In each case, it is analytically proved that the effective potential experienced by the scalar perturbation has only one maximum outside the black hole horizon and no potential well exists for the superradiance modes. So the five and six-dimensional extremal Reissner-Nordstrom black holes are superradiantly stable. In the proof, we develop a new method which is based on the Descartes' rule of signs for the polynomial equations. Our results generalize the previous study that four-dimensional extremal Reissner-Nordstrom black hole is superradiantly stable under charged massive scalar perturbation.