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Black hole immersed dark matter halo

In this work, based on the constant for the equation of state omega, we obtain the Schwarzschild-like black hole solutions in some dark matter halos. We also generalize these black hole metrics to Kerr-like black hole solutions with Newman-Janis algorithm. For an example, we derive the specific black hole space-time metrics in the case of the cold dark matter halo and Bose-Einstein condensation dark matter halo. Following the above two black hole metrics, we discuss how a dark matter halo changes the properties of black holes, including the event horizon structure (these results agree with that obtained by Liu and Zhang [Phys. Lett. B 679, 88 (2009).] in the case of gravitational collapse), stationary limit surfaces, ergosphere, and singularity structure. Our results may help us understand the interaction between the dark matter halo and supermassive black holes at the centers of galaxies.