Optical analogues to the Kerr-Newman black hole

TL;DR

This paper develops optical material analogues to Kerr-Newman black holes, enabling laboratory investigation of their properties by simulating null geodesics with feasible materials and computational methods.

Contribution

It provides exact dielectric tensors and gradient-index profiles that replicate Kerr-Newman metrics and geodesics, overcoming previous divergence issues at the horizon.

Findings

Finite material profiles are feasible with ordinary materials.

Ray tracing confirms accurate approximation of null geodesics.

Simulations demonstrate potential for laboratory black hole analogues.

Abstract

Optical analogues to black holes allow the investigation of general relativity in a laboratory setting. Previous works have considered analogues to Schwarzschild black holes in an isotropic coordinate system; the major drawback is that required material properties diverge at the horizon. We present the dielectric permittivity and permeability tensors that exactly reproduce the equatorial Kerr-Newman metric, as well as the gradient-index material that reproduces equatorial Kerr-Newman null geodesics. Importantly, the radial profile of the scalar refractive index is finite along all trajectories except at the point of rotation reversal for counter-rotating geodesics. Construction of these analogues is feasible with available ordinary materials. A finite-difference frequency-domain solver of Maxwell's equations is used to simulate light trajectories around a variety of Kerr-Newman black holes. For reasonably sized experimental systems, ray tracing confirms that null geodesics can be well-approximated in the lab, even when allowing for imperfect construction and experimental error.