# Boosted Kerr black hole in the presence of plasma

## TL;DR

This paper calculates how light bends around a moving Kerr black hole in plasma environments, considering various plasma distributions and the effects of black hole motion on gravitational lensing.

## Contribution

It introduces a method to compute light deflection angles for boosted Kerr black holes in plasma, incorporating the effects of black hole motion and plasma distributions.

## Key findings

- Black hole boost and plasma distribution affect deflection angles.
- Magnification varies with plasma type and black hole motion.
- The study provides insights into gravitational lensing in realistic astrophysical settings.

## Abstract

In this work, we obtain the deflection angle for a boosted Kerr black hole in the weak field approximation using the optics in a curved spacetime developed by J.L. Synge in 1960. We study the behavior of light in the presence of plasma by considering different distributions: uniform plasma, singular isothermal sphere, non-singular isothermal gas sphere, and plasma in a galaxy cluster. We found that the dragging of the inertial system along with the boosted parameter $\Lambda$ affect the value of the deflection angle. As an application, we studied the magnification for both uniform and singular isothermal distributions.