Photons propagating in a plasma acquire an effective mass $\mu$, which is given by the plasma frequency and which scales with the square root of the plasma density. As noted previously by Conlon and Herdeiro, for electron number densities $n_e\sim 10^{-3}$ cm$^{-3}$ (such as those measured in the interstellar medium) the effective mass induced by the plasma is $\mu \sim 10^{-12}$ eV. This would cause superradiant instabilities for spinning black holes of a few tens of solar masses. An obvious problem with this picture is that densities in the vicinity of black holes are much higher than in the interstellar medium because of accretion. We have conducted numerical simulations of the superradiant instability in spinning black holes surrounded by a plasma with density increasing closer to the black hole, in order to mimic the effect of accretion. While we confirm that superradiant instabilities appear for plasma densities that are sufficiently low near the black hole, we find that astrophysically realistic accretion disks are unlikely to trigger such instabilities.

中文翻译：

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等离子体驱动超辐射不稳定性的数值研究

在等离子体中传播的光子获得有效质量 $\mu$，该质量由等离子体频率给出并且与等离子体密度的平方根成比例。正如 Conlon 和 Herdeiro 之前所指出的，对于电子数密度 $n_e\sim 10^{-3}$ cm$^{-3}$（例如在星际介质中测量的那些），等离子体诱导的有效质量为 $ \mu \sim 10^{-12}$ eV。这将导致旋转几十个太阳质量的黑洞的超辐射不稳定性。这张图片的一个明显问题是，由于吸积作用，黑洞附近的密度比星际介质中的密度高得多。为了模拟吸积效应，我们对被等离子体包围的旋转黑洞的超辐射不稳定性进行了数值模拟，密度在靠近黑洞处增加。