# Frequency response of space-based interferometric gravitational-wave detectors

## TL;DR

This paper derives analytical formulas for the antenna response functions of space-based interferometric gravitational-wave detectors for all six polarizations, analyzing their frequency-dependent behavior and implications for signal detection.

## Contribution

It provides the first comprehensive analytical expressions for the response functions of such detectors across all polarization modes, including high-frequency behavior.

## Key findings

- Response functions decrease at high frequencies, reducing signal-to-noise ratio.
- Tensor and breathing modes fall off as 1/f^2 at high frequencies.
- Longitudinal mode response decreases as 1/f, vector mode as ln(f)/f^2.

## Abstract

Gravitational waves are perturbations of the metric of space-time. Six polarizations are possible, although general relativity predicts that only two such polarizations, tensor plus and tensor cross are present for gravitational waves. We give the analytical formulas for the antenna response functions for the six polarizations which are valid for any equal-arm interferometric gravitational-wave detectors without optical cavities in the arms.The response function averaged over the source direction and polarization angle decreases at high frequencies which deteriorates the signal-to-noise ratio registered in the detector. At high frequencies, the averaged response functions for the tensor and breathing modes fall of as $1/f^2$, the averaged response function for the longitudinal mode falls off as $1/f$ and the averaged response function for the vector mode falls off as $\ln(f)/f^2$.