  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%.
