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

TL;DR

This study investigates how perfect fluid dark matter halos affect gravitational lensing around Schwarzschild and Reissner-Nordström black holes, providing analytical and numerical insights into deflection angles, photon spheres, and black hole shadows.

Contribution

It offers the first comprehensive analytical and numerical analysis of dark matter's influence on gravitational lensing near black holes beyond leading order.

Findings

Dark matter significantly alters gravitational deflection angles.

Dark matter impacts black hole shadow sizes and photon spheres.

Analytical expansions improve understanding of lensing in dark matter environments.

Abstract

Dark matter and dark energy dominate the behavior of our universe. The dark matter usually forms halo structures 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 gravitational lensing of black holes immersed in dark matter halos is presented. To effectively model the supermassive black hole in a galaxy center (which is surrounded by dark matter halo) in a simple way, we investigate the Schwarzschild black hole and charged Reissner-Nordstr\"om black hole immersed in a perfect fluid dark matter halo. In the present work, several basic quantities in gravitational lensing (the gravitational deflection angle of light, photon sphere, black hole shadow radius, gravitational lens equation and Einstein ring) are calculated and analyzed analytically and numerically. A second order analytical expansion of gravitational deflection angle is obtained in the weak deflection limit, and the full gravitational deflection angle (including all order perturbation contributions applicable to both weak and strong deflection limits) is also calculated numerically as comparisons. It enables us to analyze the perfect fluid dark matter influences on gravitational deflection angle and gravitational lensing beyond the leading order, which were not sufficiently studied in previous works. Assuming $M \sim \lambda_{\text{DM}} \sim Q$, our results show that dark matter can greatly influence the gravitational lensing of central black holes.