Strong deflection limit analysis of black hole lensing in inhomogeneous plasma

TL;DR

This paper develops an analytical framework for understanding how non-uniform plasma affects strong gravitational lensing around black holes, revealing that plasma density profiles diminish the size and brightness of higher-order images.

Contribution

It introduces a novel analytical approach to analyze the impact of non-uniform plasma on strong deflection gravitational lensing, extending previous homogeneous plasma models.

Findings

Non-uniform plasma reduces the angular size of higher-order images.

Non-uniform plasma decreases the magnifications of these images.

The framework applies to various plasma density profiles and spacetime geometries.

Abstract

This paper investigates gravitational lensing effects in the presence of plasma in the strong deflection limit, which corresponds to light rays circling around a compact object and forming higher-order images. While previous studies of this case have predominantly focused on the deflection of light in a vacuum or in the presence of a homogeneous plasma, this work introduces an analytical treatment for the influence of a non-uniform plasma. After recalling the exact expression for the deflection angle of photons in a static, asymptotically flat and spherically symmetric spacetime filled with cold non-magnetized plasma, a strong deflection limit analysis is presented. Particular attention is then given to the case of a Schwarzschild spacetime, where the deflection angle of photons for different density profiles of plasma is obtained. Moreover, perturbative results for an arbitrary power-law radial density profile are also presented. These formulae are then applied to the calculation of the positions and magnifications of higher-order images, concluding that the presence of a non-uniform plasma reduces both their angular size and their magnifications, at least within the range of the power-law indices considered. These findings contribute to the understanding of gravitational lensing in the presence of plasma, offering a versatile framework applicable to various asymptotically flat and spherically symmetric spacetimes.