Optical refractive index and spacetime geometry

TL;DR

This paper extends the analogy between classical mechanics and optics to relativistic regimes, enabling the simulation of spacetime geometry through tailored optical media with specific refractive index profiles.

Contribution

It introduces a generalized framework connecting optical refractive index with spacetime geometry, expanding the F = ma analogy to relativistic conditions.

Findings

Optical media can mimic relativistic spacetime effects.

A dictionary linking refractive index and spacetime metric is developed.

The approach enables simulation of gravitational fields using optics.

Abstract

Classical mechanics and geometrical optics are deeply connected with each other. In this work, we generalize the analogy between these two disciplines to relativistic conditions. Using this analogy, we are able to make light follow the orbits of massive or massless particles in gravitational field, by designing a particular optical medium with a prescribed refractive index profile according to spacetime geometry. Furthermore, we build the dictionary that connects optical refractive index and spacetime metric, thus extending F = ma optics to the relativistic limit. The results shed light on the equivalence between the dielectric properties of optical media and the geometric structure of spacetime.