Distortions of images of Schwarzschild lensing
  We model the supermassive dark object $M87^*$ as a Schwarzschild lens and
study the variations in tangential, radial, and total (the product of
tangential and radial) magnifications of images (primary, secondary, and
relativistic) against the changes in angular source position and the ratio of
lens-source to the observer-source distance. Further, we study the behavior of
partial derivatives (with respect to the angular source position) of total
magnifications of images against the angular source position. Finally, we model
supermassive dark objects at centers of forty galaxies as Schwarzschild lenses
and study the variations in tangential, radial, and total magnifications of
images against the change in the ratio of mass of the lens to its distance.
These studies yield many non-intuitive results which are likely to be
significant for ngEHT observations. We {\em hypothesize} that there exists a
distortion parameter such that their signed sum of all images of singular
gravitational lensing of a source identically vanishes. We test this with
images of Schwarzschild lensing in weak and strong gravitational fields and
find that this aesthetically appealing hypothesis succeeds with flying colors.
