Analytic study of superradiant stability of Kerr–Newman black holes under charged massive scalar perturbation
Jun-Huai Xu, Zi-Han Zheng, Ming-Jian Luo, Jia-Hui Huang
Abstract
Abstract The superradiant stability of a Kerr–Newman black hole and charged massive scalar perturbation is investigated. We treat the black hole as a background geometry and study the equation of motion of the scalar perturbation. From the radial equation of motion, we derive the effective potential experienced by the scalar perturbation. By a careful analysis of this effective potential, it is found that when the inner and outer horizons of Kerr–Newman black hole satisfy $$\frac{r_-}{r_+}\leqslant \frac{1}{3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:msub> <mml:mi>r</mml:mi> <mml:mo>-</mml:mo> </mml:msub> <mml:msub> <mml:mi>r</mml:mi> <mml:mo>+</mml:mo> </mml:msub> </mml:mfrac> <mml:mo>⩽</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>3</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> and the charge-to-mass ratios of scalar perturbation and black hole satisfy $$ \frac{q}{\mu }\frac{Q}{ M}>1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:mi>q</mml:mi> <mml:mi>μ</mml:mi> </mml:mfrac> <mml:mfrac> <mml:mi>Q</mml:mi> <mml:mi>M</mml:mi> </mml:mfrac> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , the Kerr–Newman black hole and scalar perturbation system is superradiantly stable.