Time Delay of Light in the Gravitational lensing of Supermassive Black Holes in Dark Matter Halos

The dark matter halo has non-negligible effects on the gravitational lensing of supermassive black hole in the galaxy center. Our work gives a study on the time-delay of light in gravitational lensings of black holes enclosed by dark matter halos. To provide a precise description on the distribution of dark matter in galaxies, we choose several famous phenomenological dark matter halo models in astrophysics, including the NFW, Beta, Burkert and Moore models, to carry out the present study. Through numerically calculating the time-delay of light in gravitational lensing, a comparative analysis of the dark matter effects within different halo models has been performed. Assuming typical length scales associated with the galactic gravitational lensing, numerical results indicate that the NFW, Beta, Moore dark matter halos can significantly enhance the time delay of light. Conversely, the dark matter in Burkert model exhibits a negative contribution on the time delay, resulting in smaller time delay compared with those for pure black hole cases. Keywords: Black Hole; Gravitational Lensing; Time Delay; Dark Matter Halo