There are strong interests in considering ultra-light scalar fields (especially axion) around a rapidly rotating black hole because of the possibility of observing gravitational waves from axion condensate (axion cloud) around black holes. Motivated by this consideration, we propose a new method to study the dynamics of an ultra-light scalar field with self-interaction around a rapidly rotating black hole, which uses the dynamical renormalization group method. We find that for relativistic clouds, saturation of the superradiant instability by the scattering of the axion due to the self-interaction does not occur in the weakly non-linear regime when we consider the adiabatic growth of the cloud from a single superradiant mode. This may suggest that for relativistic axion clouds, an explosive phenomenon called the Bosenova may inevitably happen, at least once in its evolutionary history.

中文翻译：

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自相互作用轴子云超辐射生长的重整化群分析

考虑快速旋转的黑洞周围的超轻标量场（尤其是轴子）引起了浓厚的兴趣，因为有可能观察黑洞周围轴子凝聚物（轴子云）的引力波。出于这种考虑，我们提出了一种新方法来研究快速旋转黑洞周围具有自相互作用的超轻标量场的动力学，该方法使用动态重整化群方法。我们发现，对于相对论云，当我们从单一超辐射模式考虑云的绝热生长时，由于自相互作用导致的轴子散射导致的超辐射不稳定性饱和不会发生在弱非线性区域。这可能表明，对于相对论轴子云，可能不可避免地会发生一种称为 Bosenova 的爆炸现象，