Cartographic distortions make dielectric spacetime analog models imperfect mimickers

TL;DR

This paper demonstrates that dielectric spacetime analog models cannot perfectly mimic vacuum spacetime light propagation due to inherent distortions, revealing limitations in their use for transformation optics and proposing a related formulation to address these issues.

Contribution

It analyzes the covariance and kinematics of dielectric analog spacetimes, showing the impossibility of distortion-free emulation of all features and proposing a formulation that mitigates these limitations.

Findings

Not all features of vacuum spacetime can be simultaneously emulated in dielectric analogs.

Distortions are inherent due to the covariance properties of the analog models.

A specific formulation of transformation optics can address the limitations identified.

Abstract

It is commonly assumed that if the optical metric of a dielectric medium is identical to the metric of a vacuum space-time then light propagation through the dielectric mimics light propagation in the vacuum. However, just as the curved surface of the Earth cannot be mapped into a flat plane without distortion of some surface features, so too is it impossible to project the behavior of light from the vacuum into a dielectric analog residing in Minkowski space-time without introducing distortions. We study the covariance properties of dielectric analog space-times and the kinematics of a congruence of light in the analog, and show how certain features can be faithfully emulated in the analog depending on the choice of projection, but that not all features can be simultaneously emulated without distortion. These findings indicate conceptual weaknesses in the idea of using analog space-times as a basis for transformation optics, and we show that a certain formulation of transformation optics closely related to analog space-times resolves these issues.