Guided Waves in Static Curved Spacetimes

TL;DR

This paper develops a covariant formalism for analyzing guided electromagnetic waves in static curved spacetimes, enabling studies of wave propagation in gravitational fields with potential applications in relativity and quantum optics.

Contribution

It introduces a novel covariant Hertzian potential approach for describing guided modes in static curved spacetimes, including cutoff frequencies and special TEM modes.

Findings

Derived wave equations for TE and TM modes in curved spacetime

Applied formalism to Schwarzschild spacetime example

Provided a framework for studying electromagnetic guidance in gravitational fields

Abstract

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.