Periodic orbits and plasma effects on gravitational weak lensing by self-dual black hole in loop quantum gravity

Abstract

In this paper, we study the geodesics, periodic orbits, and plasma effects on gravitational weak lensing around the self-dual black hole in loop quantum gravity characterized by the parameter $ϵ$. We determine the marginal bound orbits (MBO) and innermost stable circular orbits (ISCO) around the self-dual black hole and show that these orbits decrease with an increase in the parameter $ϵ$. Interestingly, we also observe that the energy increase but the angular momentum of the ISCO decrease with an increasing $ϵ$. We further examine periodic orbits of massive particles that involve a rational number represented by a triplet of integers and show that, for a constant rational number, the energy becomes lower as a consequence of the presence of the parameter $ϵ$. Finally, we delve into the impact of the quantum correction parameter $ϵ$ and the plasma effects on the deflection angle and the total magnification of lensed images. We show that the deflection angle decreases under the influences of both the parameter $ϵ$ and the non-uniform plasma frequency, but it increases due to the impact of uniform plasma.