Metamaterial analog of a black hole shadow: An exact ray-tracing simulation based on the spacetime index of refraction

TL;DR

This paper demonstrates an exact ray-tracing simulation method for metamaterial analogs of black holes, showing that photon spheres and shadows can be accurately modeled using a spacetime index of refraction in flat spacetime.

Contribution

It introduces a novel exact simulation technique linking null geodesics in curved spacetime to light trajectories in metamaterials via the spacetime index of refraction.

Findings

Photon spheres in metamaterials match black hole predictions

Black hole shadows can be simulated in metamaterials

Ray-tracing accurately reproduces black hole optical features

Abstract

In this letter first we show that the equation of null geodesics in spherically symmetric spacetimes in isotropic coordinates is identical to the equation of light ray trajectories in isotropic media in flat spacetime. Based on this analogy we introduce an exact simulation of the light ray trajectories both in these spacetimes and in their metamaterial analogs in terms of the spacetime index of refraction. As unstable light trajectories, the photon spheres form in these metamaterial analogs at {\it exactly} the same radial distances as expected from the corresponding black hole geometries. Using the same ray-tracing simulation we find the analog of a simple black hole shadow formed by the metamaterial analog of a Schwarzschild black hole, eclipsing a line of light sources near its analog horizon.