Quartic Scalar Clouds on Fixed Kerr Backgrounds
arXiv:2607.28044
The paper investigates stationary nonlinear scalar field configurations (Q‑clouds) on fixed Kerr and Schwarzschild black hole backgrounds, analyzing quartic and axion‑inspired potentials and mapping the regions where such clouds exist.
Abstract
We study stationary nonlinear clouds of a complex scalar field on fixed Kerr and Schwarzschild backgrounds, with an unbounded scalar potential. On Kerr backgrounds we find finite-amplitude Q-clouds satisfying the synchronisation condition $Ï=mΩ_H$. They occupy two-dimensional regions of the ($Ω_H,M_K$) plane and reduce to the corresponding linear clouds as the scalar field amplitude tends to zero. The quartic domain can continue to $Ω_H=0$, where both the synchronised frequency and the Noether charge vanish and the solutions become static nonlinear scalar clouds on a fixed Schwarzschild background. We also compute the existence domain for a normalised, axion-inspired cosine potential.