Can continuous density profile correctly describe strong gravitational lensing?

TL;DR

This paper questions whether continuous density profiles accurately model lens galaxies in strong gravitational lensing, suggesting that discrete profiles may increase magnification without affecting image positions, with future gravitational wave observations as a test.

Contribution

It highlights the potential discrepancy between continuous and discrete density profiles in lens modeling and proposes gravitational wave observations as a future test.

Findings

Discrete density profiles increase magnification in lensing.

Image positions remain unchanged between models.

Future gravitational wave observations can test these effects.

Abstract

Strong gravitational lensing is an important tool to probe the universe. In the theoretical analysis of gravitational lensing, it is assumed that continuous density profile can correctly describe the lens galaxy. But in fact this assumption has never been rigorously tested. In this paper, we discuss this issue, and point out that if we use discrete density profile to model the lens galaxy, then the position of the images does not change, but the magnification will be increased. Strongly lensed gravitational waves could test this conclusion in the future.