Eur. Phys. J. C (2024) 84: 136
https://doi.org/10.1140/epjc/s10052-024-12492-4

Regular Article - Theoretical Physics

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

¹ College of Physics, Guizhou University, 550025, Guiyang, China
² School of Mathematics and Statistics, Guizhou University of Finance and Economics, 550025, Guiyang, China

^d zwlong@gzu.edu.cn

Received: 30 November 2023
Accepted: 28 January 2024
Published online: 8 February 2024

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.