Time travel in transformation optics: Metamaterials with closed null geodesics

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.

Transformation Optics: From Classic Theory and Applications to its New Branches

“…it may involve a time-varying medium, an electric-magnetic coupling medium, etc.). We can obtain more innovative devices by introducing time-related coordinate transformations, including space-time cloaks, [114][115][116] event carpets, [117] time traveling, [118] etc. [119] The theory of TO has also been further developed and refined in recent years.…”

“…it may involve a time‐varying medium, an electric–magnetic coupling medium, etc.). We can obtain more innovative devices by introducing time‐related coordinate transformations, including space–time cloaks, event carpets, time traveling, etc …”

Covariant kinematics of light in media and a generalized Raychaudhuri equation

“…light propagation near black holeswith some kind of laboratory-accessible system [8][9][10][11][12][13][14]. Mathematically, they are very naturally related to ideas in transformation optics and metamaterials [15][16][17][18][19][20], which has resulted in a great deal of cross-fertilization of ideas. The tensorial, differential forms formulation of electrodynamics used here is also very closely related to developments in the premetric electrodynamics program, which seeks a deeper understanding of the structure and pliability of electrodynamics by considering the metric as a subsidiary field that does not directly enter into Maxwell's equations [21,22].…”

Cartographic distortions make dielectric spacetime analog models imperfect mimickers

“…Later, Plebanski identified the effective permittivity and permeability of an arbitrary space-time metric [7], and these results were used by de Felice to describe a dielectric representation of Schwarzschild space-time, arguably the first definite description of an analog black hole [8]. In the last decade, developments in metamaterials [9][10][11][12][13] have opened the possibility of physically realizing artificial media possessing some of the unusual dielectric properties required to construct a dielectric analog space-time and has sparked a resurgence of interest in the subject [14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”