Guided Waves in Static Curved Spacetimes

This work investigates the propagation of electromagnetic waves in waveguides within static curved spacetimes. We develop a covariant formalism using Hertzian potentials to describe guided electromagnetic modes in spacetimes with metrics that depend on the proper length along the waveguide axis. The Maxwell equations are solved using a Hertzian potential ansatz, resulting in wave equations for TE and TM modes. We analyze the axial and transverse components of the solutions and derive expressions for the cutoff frequency and guide wavelength. The special case of TEM modes is also examined. As an illustrative example, we apply the formalism to radial propagation in Schwarzschild spacetime. This work provides a framework for studying guided electromagnetic waves in curved spacetime geometries, opening up potential applications in precision tests of general relativity and relativistic quantum optics.