Abstract In this paper, we investigate the existence of stationary scalar clouds in the magnetized Kerr black hole background within the framework of Einstein–Maxwell theory. We consider the dynamics of a massive, charged test scalar field governed by the Klein–Gordon equation. Under the assumption of a weak magnetic field, we demonstrate that the Klein–Gordon equation admits separable solutions in radial and angular variables. The angular equation reduces to a generalized spheroidal harmonic form, while the radial equation can be expressed in terms of the double confluent Heun function. By analyzing the asymptotic behavior of the radial solution, we establish the existence of bound-state scalar clouds characterized by a discrete mass spectrum. We further outline how the (quasi)bound spectrum can be extracted using the continued-fraction method of Vieira–Bezerra–Kokkotas (VBK).
Haryanto M. Siahaan (2025) studied this question.