Gravitational lensing by eigenvalue distributions of random matrix models

TL;DR

This paper explores how eigenvalue densities from unitary random matrix ensembles can model mass distributions in gravitational lensing, enabling analytical solutions and applications to galaxy systems.

Contribution

It introduces a novel approach using random matrix eigenvalue densities as mass distributions in gravitational lensing models, with analytical solutions for complex lens equations.

Findings

Eigenvalue densities can effectively model galaxy lensing systems.

Analytical solutions are obtained for lens equations in complex plane.

Models are applicable to edge-on galaxy systems.

Abstract

We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We prove that these models can be applied to describe lensing by systems of edge-on galaxies. We illustrate our analysis with the Gaussian and the quartic unitary matrix ensembles.