Weak Gravitational Lensing of Schwarzschild and Charged Black Holes Embedded in Perfect Fluid Dark Matter Halo

The dark matter and dark energy dominate the behavior of our universe. The unknown dark matter usually forms halos in large number of galaxies. Properties of dark matter halo can be revealed and understood from the gravitational lensing observations. In this work, a comprehensive study on the weak gravitational lensing of black hole embedded in dark matter halos is presented. To effectively model the supermassive black hole in galaxy center (which is surrounded by dark matter halo) in a simple way, we use the Schwarzschild black hole and charged Reissner-Nordström black hole embedded in a perfect fluid dark matter halo. In the present work, several key quantities in weak gravitational lensing (gravitational deflection angle of light, photon sphere, black hole shadow radius, gravitational lens equation and Einstein ring) are calculated and analyzed analytically and numerically. The results in our work indicate that the dark matter can greatly influence the gravitational lensing of central black holes.