In this Letter, we present five analytical models in closed forms, each representing a supermassive black hole (SMBH) located at the center of a galaxy surrounded by dark matter (DM) halo. The density profile of the halo vanishes inside twice the Schwarzschild radius of the hole and satisfies the weak, strong, and dominant energy conditions. The spacetime are asymptotically flat, and the difference among the models lies in the slopes of the density profiles in the spike and regions far from the center of the galaxy. Three of them represent cusp models, whereas the other two represent core models. With the well-known (generalized) Newman-Janis algorithm, rotating SMBHs with DM halos can be easily constructed from these models.

中文翻译：

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被暗物质晕包围的星系中超大质量黑洞的分析模型


在这封信中，我们提出了五个封闭形式的分析模型，每个模型代表一个位于被暗物质（DM）光环包围的星系中心的超大质量黑洞（SMBH）。光晕的密度分布在两倍史瓦西半径的空穴内消失，并满足弱、强和主导能量条件。时空是渐近平坦的，模型之间的差异在于尖峰和远离星系中心的区域的密度剖面的斜率。其中三个代表尖点模型，另外两个代表核心模型。利用众所周知的（广义）Newman-Janis 算法，可以根据这些模型轻松构建具有 DM 光环的旋转SMBH。