Instability of Massive Scalar Fields in Kerr-Newman Spacetime

TL;DR

This paper studies the instability of charged massive scalar fields around Kerr-Newman black holes, revealing that super-radiance causes exponential growth of the field amplitude, with numerical results surpassing previous analytic estimates.

Contribution

It provides numerical calculations of scalar field growth rates in Kerr-Newman spacetime, showing larger maximum instability than earlier analytic predictions.

Findings

Scalar fields exhibit super-radiant instability in Kerr-Newman spacetime.

Numerical growth rates are up to three times larger than analytic estimates.

Electric charge influences the instability strength.

Abstract

We investigate the instability of charged massive scalar fields in Kerr-Newman spacetime. Due to the super-radiant effect of the background geometry, the bound state of the scalar field is unstable, and its amplitude grows in time. By solving the Klein-Gordon equation of the scalar field as an eigenvalue problem, we numerically obtain the growth rate of the amplitude of the scalar field. Although the dependence of the scalar field mass and the scalar field charge on this growth rate agrees with the result of the analytic approximation, the maximum value of the growth rate is three times larger than that of the analytic approximation. We also discuss the effect of the electric charge on the instability of the scalar field.