Fully metallic geodesic lenses as analog electromagnetic models of static and spherically symmetric gravitational fields

TL;DR

This paper presents a fully metallic waveguide model that simulates static, spherically symmetric gravitational fields by mimicking null geodesics, enabling electromagnetic analogs of black holes and wormholes with high accuracy.

Contribution

It introduces a novel metallic waveguide design that replicates space-time metrics of gravity models without refractive media, using shape tailoring to emulate null geodesics.

Findings

Successfully modeled Schwarzschild black hole and wormhole metrics

Achieved null geodesic path replication with less than 4% error

Demonstrated full-wave simulation validation of the analog model

Abstract

We demonstrate that a fully metallic and air-filled geodesic waveguide can be employed as an analog electromagnetic model of a static and spherically symmetric gravitational field. By following the Plebanski formalism, a space-time metric of the aforementioned type is firstly encoded into the electromagnetic properties of a flat space-time region in the form of an isotropic and radially varying refractive index distribution. Then, a three-dimensional, air-filled, and axially symmetric waveguide, composed of two equally spaced and curved metallic surfaces, is employed. Its shape is tailored such that the effective paths, followed by transverse electromagnetic beams of microwave radiation within this waveguide, result equivalent to null-geodesics taking place in the aforementioned refractive medium. This strategy avoids the need for a refractive medium, although it only allows to reproduce the space-time metric on the invariant plane. Two analog electromagnetic models of gravity, using the proposed approach, are designed to reproduce the metric of both a Schwarzschild black hole and a Morris-Thorne wormhole. The results from full-wave simulations demonstrate that a one-dimensional Gaussian beam faithfully follows a path completely equivalent to general relativistic null geodesics with a mean relative error within 4%.