Strong deflection limit analysis of black hole lensing in inhomogeneous plasma

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.