Analytical study of gravitational lensing in Kerr-Newman black-bounce spacetime

Abstract

We investigate the equatorial deflection angle of light rays propagating in Kerr-Newman black-bounce spacetime. Furthermore, we analyze the light ray trajectories and derive a closed-form formula for deflection angle in terms of elliptic integrals. The deflection angle increases with the decrease of charge and regularisation parameter for a particular impact parameter. We also study the strong field limit of the deflection angle. Using this strong deflection angle formula and lens equation, we find the radius of the first Einstein ring and study its dependence on the charge and the regularisation parameter. We demonstrate that the charge has a robust effect on the size of the Einstein rings, but the effect of the regularization parameter on the ring size is negligible. We also investigate the non-equatorial lensing and the caustic structures for small polar inclination, and the same observations appear to hold. These results directly affect the observational appearance of the Kerr-Newman black-bounce.

A review on analytical studies in gravitational lensing

“…We will also discuss the strong deflection angle's analytical form. We will closely follow the notation in [120].…”

“…We start by applying the general formalism of lensing in this special kind of axisymmetric non-singular spacetime. We will closely follow the notation of [120] throughout this section.…”

“…, which are incomplete and complete elliptic integrals of the second kind, respectively. The computation details are given in [120]. So, similar to the Kerr-Newman case, we provide an analytical expression of the equatorial deflection angle for the Kerr-Newman black-bounce metric upto O(l 2 ) in this section.…”

“…In the leftmost figure, we vary l keeping a and Q fixed. In the middle figure, we vary a keeping l and Q, and in the rightmost figure, we vary Q keeping a and l [120].…”

“…When the solution does not admit any horizon, it corresponds to a wormhole solution. Recently, the gravitational lensing in the strong deflection limit for these blackbounce spacetimes has been studied [120,[138][139][140][141]. From the lensing perspective, this kind of spacetime provides us with extra tunable parameters; hence, it is interesting to investigate the effect of this extra parameter from the theoretical and observational points of view.…”