Modeling the black holes surrounded by a dark matter halo in the galactic center of M87

Abstract

In this paper, the structure of a dark matter halo can be well described by the mass model of M87 and the Einasto profile for the cold dark matter model, i.e., ${\rho }_{\text{eina}}(r)={\rho }_{\text{e}}\exp (-2{\alpha }^{-1}((r/r_{\text{e}}{)}^{\alpha }-1))$ (Wang et al. in Nature 585:39-42, 2020). Under these conditions, we construct a solution of a static spherically symmetric black hole in a dark matter halo. Then, using the Newman-janis algorithm, we extend this static solution to the case of rotation, and obtain a solution for the Kerr-like black hole. We prove that this solution of the Kerr-like black hole is indeed a solution to the Einstein field equations. Finally, taking M87 as an example, we study and analyze some physical properties of this Kerr-like black hole, and then compare them with the Kerr black hole. Particularly, from the perspective of the black hole shadow and the fact that the Kerr-like black hole and the Kerr black hole is distinguishable, we give the upper limit of the shape parameter of the Einasto density profile, that is approximately $\alpha <0.22$, which may provide a new method to further improve and perfect the density profile of dark matter model. These research results for the black hole in a dark matter halo may indirectly provide an effective method for detecting the existence of dark matter.

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• Probing the black holes in a dark matter halo of M87 using gravitational wave echoes
• Shadows and Observational Images of a Schwarzschild-like Black Hole Surrounded by a Dehnen-type Dark Matter Halo
• Shadow of Kerr black hole surrounded by a cloud of strings in Rastall gravity and constraints from M87*
• Gravitational Lensing of Euler-Heisenberg Black Hole Surrounded by Perfect Fluid Dark Matter
• Probing black holes via quasinormal modes in a dark energy-induced dark matter
• Beyond general relativity: gravitational waves in non-minimally coupled theories