Conservation of distortion of gravitationally lensed images

Abstract

We recently hypothesized that a distortion parameter exists such that its signed sum for all images of singular gravitational lensing of a source vanishes identically [K. S. Virbhadra, Phys. Rev. D {\bf 106}, 064038 (2022)]. We found a distortion parameter (the ratio of the tangential to radial magnifications) that satisfied the hypothesis for the images of Schwarzschild lensing with flying colors. We now show that another distortion parameter (the difference of tangential and radial magnifications) also magnificently supports our hypothesis when we perform computations with the primary-secondary and relativistic images. The distortion parameters, which satisfy the aesthetically appealing hypothesis, will likely aid in developing gravitational lensing theory. Finally, we discuss the conservation of distortion of images in gravitational lensing.