A method to measure a relative transverse velocity of source-lens-observer system using gravitational lensing of gravitational waves

TL;DR

This paper proposes a method to measure the relative transverse velocity of a source-lens-observer system using gravitational lensing effects on gravitational waves, leveraging interference patterns detectable by future space-based detectors.

Contribution

It introduces a novel approach to extract relative transverse velocity information from gravitational wave lensing interference, which has not been previously explored.

Findings

Interference among lensed gravitational waves encodes velocity information.

Future space-borne detectors like BBO/DECIGO could measure this effect.

Potential to enhance understanding of source-lens-observer dynamics.

Abstract

Gravitational waves propagate along null geodesics like light rays in the geometrical optics approximation, and they may have a chance to suffer from gravitational lensing by intervening objects, as is the case for electromagnetic waves. Long wavelength of gravitational waves and compactness of possible sources may enable us to extract information in the interference among the lensed images. We point out that the interference term contains information of relative transverse velocity of the source-lens-observer system, which may be obtained by possible future space-borne gravitational wave detectors such as BBO/DECIGO.