Analytical models of supermassive black holes in galaxies surrounded by dark matter halos

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.

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