Analytical Kerr-Sen dilaton-axion black hole lensing in the weak deflection limit

Abstract

We investigate analytical gravitational lensing by charged, stationary, axially symmetric Kerr-Sen dilaton-axion black holes in the weak-deflection limit. Approximate solutions to the lightlike equations of motion are present up to and including third-order terms in $M/b$, $a/b$, and ${r}_{\ensuremath{\alpha}}/b$, where $M$ is the black hole mass, $a$ is the angular momentum, ${r}_{\ensuremath{\alpha}}={Q}^{2}/M$, $Q$ being the charge and $b$ is the impact parameter of the light ray. We compute the positions of the two weak field images, the corresponding signed and absolute magnifications up to post-Newtonian order. It is shown that there are static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are functions of the charge. The shift of the critical curves as a function of the lens angular momentum is found, and it is shown that they decrease slightly with the increase of the charge. The pointlike caustics drift away from the optical axis and do not depend on the charge. All of the lensing quantities are compared to particular cases as Schwarzschild and Kerr black holes as well as the Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole.