A Michelson interferometer in the field of a plane gravitational wave

TL;DR

This paper analyzes how a Michelson interferometer responds to a plane gravitational wave within general relativity, deriving delay formulas that match linearized Einstein-Maxwell solutions and extending to quadratic order.

Contribution

It provides a detailed derivation of light delay in a Michelson interferometer affected by gravitational waves using Hamilton-Jacobi formalism, including higher-order approximations.

Findings

Delay formula matches linearized Einstein-Maxwell results

Derived quadratic approximation for light delay

Confirms interferometer response to gravitational waves

Abstract

We treat the problem of a Michelson interferometer in the field of a plane gravitational wave in the framework of general relativity. The arms of the interferometer are regarded as the world lines of the light beams, whose motion is determined by the Hamilton-Jacobi equation for a massless particle. In the case of a weak monochromatic wave we find that the formula for the delay of a light beam agrees with the result obtained by solving the linearized coupled Einstein-Maxwell equations. We also calculate this delay in the next (quadratic) approximation.