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arXiv · 2607.28044

Quartic Scalar Clouds on Fixed Kerr Backgrounds

Hendrik Mennenga
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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 $\omega=m\Omega_H$. They occupy two-dimensional regions of the ($\Omega_H,M_K$) plane and reduce to the corresponding linear clouds as the scalar field amplitude tends to zero. The quartic domain can continue to $\Omega_H=0$, 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.

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Hendrik Mennenga. 2026-07-30. Quartic Scalar Clouds on Fixed Kerr Backgrounds. https://arxiv.org/abs/2607.28044

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