We show that there exist steady states of the spherically symmetric massless Einstein–Vlasov system which surround a Schwarzschild black hole. The steady states are (thick) shells with finite mass and compact support. Furthermore we prove that an arbitrary number of shells, necessarily well separated, can surround the black hole. To our knowledge this is the first result of static self-gravitating solutions to any massless Einstein-matter system which surround a black hole. We also include a numerical investigation about the properties of the shells.

中文翻译：

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史瓦西黑洞周围无质量爱因斯坦-弗拉索夫系统稳态的存在

我们表明存在围绕施瓦茨柴尔德黑洞的球对称无质量爱因斯坦-弗拉索夫系统的稳态。稳态是具有有限质量和紧凑支撑的（厚）壳。此外，我们证明了任意数量的壳，必须很好地分开，可以包围黑洞。据我们所知，这是围绕黑洞的任何无质量爱因斯坦物质系统的静态自引力解的第一个结果。我们还包括对壳属性的数值研究。