Anti-telephones in transformation optics: metamaterials with closed null geodesics

TL;DR

This paper explores how transformation optics can model materials that theoretically support closed null geodesics, raising questions about causality and providing detailed derivations of the required material properties.

Contribution

It introduces a theoretical framework linking transformation optics with spacetimes supporting closed null geodesics, including detailed derivations of material parameters and causality considerations.

Findings

Derived material parameters for closed null geodesic support

Demonstrated no causality violation occurs in the model

Provided full derivation of Plebanski equations for the spacetime

Abstract

We apply the methods of transformation optics to theoretical descriptions of spacetimes that support closed null geodesic curves. The metric used is based on frame dragging spacetimes, such as the van Stockum dust or the Kerr black hole. Through transformation optics, this metric is analogous to a material that in theory should allow for communication between past and future. Presented herein is a derivation and description of the spacetime and the resulting permeability, permittivity, and magneto-electric couplings that a material would need in order for light in the material to follow closed null geodesics. We also address the paradoxical implications of such a material, and demonstrate why such a material would not actually result in a violation of causality. A full derivation of the Plebanski equations is also included.