# Gauge independent response of a laser interferometer to gravitational waves

## TL;DR

This paper derives a gauge-invariant formula for a laser interferometer's response to gravitational waves, applicable in any metric theory of gravity without assuming long wavelength or specific gauge conditions.

## Contribution

It provides a gauge-independent, general expression for interferometer response to gravitational waves in any metric theory, considering all metric modes without long wavelength approximation.

## Key findings

- Response formula is gauge-invariant and observable.
- Applicable to all metric theories of gravity.
- Valid in the first order of perturbation.

## Abstract

Laser interferometer response to a plane gravitational wave on the Minkowski background is given. The derivation does not assume any particular gauge within a class compatible with almost Minkowskian coordinates that preserve a plane wave form of the solutions. Consequently all ten modes of the metric are taken into an account. The final result, the time of flight of a laser signal exchanged between freely moving observers, is expressed in the form of integrals of the metric perturbations taken along the undisturbed trajectories. The result can be applied in any metric theory o gravity; it is valid in the first order of the perturbation and does not assume the long wavelength approximation. The obtained response is shown to define an observable, i.e. it is gauge--invariant with respect to the assumed class of gauge transformations