Laboratory Frame Representation for General High-Frequency Gravitational Waveforms

TL;DR

This paper develops a comprehensive method to transform gravitational wave metrics into laboratory frames, enabling accurate detection and analysis of high-frequency GWs in next-generation experiments.

Contribution

It provides a closed-form metric transformation for chirp-like waveforms and efficient approximations for complex signals, aiding high-frequency GW detection.

Findings

Derived a closed-form expression for metric transformation.

Introduced an efficient Taylor expansion approximation.

Demonstrated application to detector response calculations.

Abstract

Next-generation gravitational wave (GW) experiments will explore higher frequency ranges, where GW wavelengths approach the size of the detector itself. In this regime, GWs may be detected not just through the well-known mechanical deformation by tidal forces but also via induced effective currents in electromagnetic background fields. However, the calculation of this signal requires the GW metric in laboratory coordinates of the detector, and an accurate transformation to all orders into this frame is necessary. In this work, we derive a closed-form expression for the metric transformation of general chirp-like waveforms expressed in terms of the transverse-traceless GW metric, its integral, and its derivative. For more complex signals, where analytical integration is impractical, we provide an efficient approximation based on Taylor expansions of the retarded time to coalescence. Finally, we demonstrate how these results can be applied to calculate the signal response of a large class of detectors. Our approach provides essential tools for designing and interpreting high-frequency GW experiments that search for compact object mergers at MHz to GHz frequencies beyond the long-wavelength limit.