Gravitational lensing by a charged spherically symmetric black hole immersed in thin dark matter

We investigate the gravitational lensing effect around a spherically symmetric black hole, whose metric is obtained from the Einstein field equation with electric charge and perfect-fluid dark matter contributing to its energy-momentum tensor. We do the calculation analytically in the weak field limit and we assume that both the charge and the dark matter are much less abundant (only give rise to the next-leading-order contribution) in comparison to the black hole mass. In particular, we derive the light deflection angle and the size of the Einstein ring, where approximations up to the next-leading order are done with extra care, especially for the logarithmic term from perfect-fluid dark matter. We expect our results will be useful in the future to relate the theoretical model of perfect fluid dark matter with observations of celestial bodies immersed in thin dark matter.

Automated summary

We investigated the gravitational lensing effect around a spherically symmetric black hole, taking into account its electric charge and perfect-fluid dark matter. Our analytical calculations in the weak field limit considered the small abundance of both the charge and the dark matter compared to the black hole mass. We obtained the light deflection angle and the size of the Einstein ring, with careful approximations for the logarithmic term from the perfect-fluid dark matter. Our results may be useful in connecting the theoretical model of perfect-fluid dark matter with observations of celestial bodies surrounded by thin dark matter.