Gravidade análoga em metamateriais: um elo entre a física da matéria condensada, gravitação e cosmologia

Abstract

The term “analogous gravity” refers to a research programme whose purpose is to investigate analogues of gravitational fields, from the perspective of general relativity, in physical systems of other areas, aiming to obtain a better understanding of both systems involved. Analogies have proved important in physics and mathematics, for an analogy taken meticulously to a specific problem may be able to suggest unexpected routes to a possible solution. Thus, examples of analogous gravitational models date back to the beginnings of general relativity. With the development of nanotechnology, an alternative to obtaining similar gravitational and cosmological models is through the study of light propagation in metamaterials. These are artificially constructed, so that their electromagnetic properties can be carefully modeled because they derive from the same artificial structure. By virtue of this freedom, it has become possible to emulate a temporal behavior in one of the three spatial coordinates, simulating, for example, a 2+1 spacetime. In this work, through a theoretical study in hyperbolic and electronic metamaterials, we establish analogous models for two systems: the compact Milne universe, which represents a simple model of cosmic singularity in cyclic cosmological models, and the signature transition between a Minkowski spacetime and a kleinian spacetime, the latter being characterized by being endowed with two time-type coordinates. In both cases, through an analysis in the framework of wave optics, we will see how the behavior of a Klein-Gordon scalar field can be reproduced in the corresponding material medium. In addition, in the context of the Milne universe, we will show that the classical behavior, that is, the timelike and spacelike geodesics can also be reproduced in the metamaterial by the trajectories described by the light rays.