考虑静态、球对称的情况, 对等离子体包围的黑洞外部解进行了细致研究. 在给出基本方程之后, 分别求出了在 ${g_{tt}}{g_{rr}} = - 1$ 和 $p = 0$ 两种近似条件下对应的解析解. 与精确数值解进行了比较, 发现前一种近似条件下的解析解更接近精确数值解. 这为在等离子体包围的情况下计算黑洞扰动的似正规模, 以及研究黑洞阴影和光子环提供了依据.

In this paper, the exterior solution for a spherically symmetric black hole surrounded by plasma is studied in detail. After deriving the fundamental governing equations, the analytic solutions under two approximate conditions, ${g_{tt}}{g_{rr}} = - 1$ and $p = 0$ , are investigated. Comparing the two results with the accurate numerical solution, we find that the former approximation offers superior accuracy. This provides a basis for studying the quasinormal modes of perturbations as well as the shadow and ring when the black hole is surrounded by plasma.