Distortions of images of Schwarzschild lensing

Abstract

We model the supermassive dark object M 87 * 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 lenssource 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 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.

Shadow, lensing, quasinormal modes, greybody bounds and neutrino propagation by dyonic ModMax black holes

“…Contrary to this, Virbhadra showed that just observation of relativistic images (no information about the masses and distances are required) gives an incredibly accurate value for the upper bound to the compactness of massive dark objects [75]. Moreover, Virbhadra hypothesized that there exists a distortion parameter such that the signed sum of all images of singular gravitational lensing of a source identically vanishes by testing this with images of Schwarzschild lensing in weak and strong gravitational fields [76].…”

Possible connection between dark matter and supermassive black holes

“…This seems to us appropriate and timely because the detection of such a shadow is well within the capabilities of the Event Horizon Telescope. Finally, while finishing this manuscript, we found some recent papers [65,66] which are relevant to our future work. In the aforementioned literature, the author shows that just the observation of relativistic images (no information about the masses and distances are required) provides an incredibly accurate value for the upper bound to the compactness of massive dark objects.…”

“…In the aforementioned literature, the author shows that just the observation of relativistic images (no information about the masses and distances are required) provides an incredibly accurate value for the upper bound to the compactness of massive dark objects. It would be a worthwhile undertaking to apply the new method developed in [65,66] in order to study the gravitational lensing signature of the new gravitational objects derived in the present work.…”

The geometry of massive particle surfaces

“…The recent publication of an image of a black hole at the center of our Galaxy [1] and Galaxy M87 [2] stimulates further interest in shadows and relativistic images of black holes as a tool for searching for new physics in the Cosmos. The shadows of black holes and images of accretion disks around them are now released in the radio and optical ranges and they are associated with the properties of null geodesics in strong gravitational fields [3][4][5][6][7][8][9][10]. The most important role in the mathematical understanding of shadows is played by the concept of characteristic photon surfaces [11][12][13][14][15][16][17][18][19][20][21] -timelike hypersurfaces, where bounded photon trajectories are lined up.…”