Eur. Phys. J. C (2013) 73: 2378
https://doi.org/10.1140/epjc/s10052-013-2378-x

Regular Article - Theoretical Physics

Stationary resonances of rapidly-rotating Kerr black holes

¹ The Ruppin Academic Center, Emeq Hefer, 40250, Israel
² The Hadassah Institute, Jerusalem, 91010, Israel

^* e-mail: shaharhod@gmail.com

Received: 28 January 2013
Published online: 9 April 2013

Abstract

The Klein–Gordon equation for a massive scalar field in the background of a rapidly-rotating Kerr black hole is studied analytically. In particular, we derive a simple formula for the stationary (marginally-stable) resonances of the field in the black-hole spacetime. The analytically derived formula is shown to agree with direct numerical computations of the resonances. Our results provide an upper bound on the instability regime of rapidly rotating Kerr black holes to massive scalar perturbations.