Massive Scalar Perturbation of Extremal Rotating Braneworld Black hole: Superradiant Stability Analysis

TL;DR

This paper investigates the superradiant stability of extremal braneworld black holes with tidal charge under massive scalar perturbations, deriving bounds on parameters for stability.

Contribution

It introduces a stability analysis specific to braneworld extremal black holes, incorporating tidal charge effects and deriving parameter bounds for superradiant stability.

Findings

Bound on tidal charge for Kerr-like black holes.

Lower bound on mass-charge ratio for Kerr-Newman black holes.

Identification of parameter space ensuring stability.

Abstract

We analyse the superradiant stability of braneworld extremal Kerr and Kerr-Newman black holes under massive scalar perturbation. These black hole solutions differ from their four dimensional counterpart by the presence of a tidal charge, which unlike electric charge, can take both positive and negative values and carries the signature of extra dimensions. We consider the perturbation of the brane geometry by a massive scalar field. From the radial equation of motion of the scalar field, we have found the effective potential felt by the field. For superradiant stability, there should not be any trapping well of the effective potential outside of the horizon. Using this condition we have specified the parameter space of superradiant stability which depends on parameters of both black hole and perturbation. In the case of Kerr-like extremal braneworld black holes, we have obtained a bound on tidal charge for superradiant stability under a massive scalar perturbation. Similarly, for slowly rotating Kerr-Newman like extremal braneworld black holes, we have obtained a lower bound of the product of mass to charge ratio of the black hole and scalar field, for which the system is superradiantly stable.