# How does the Earth's rotation affect predictions of gravitational wave strong lensing rates?

## TL;DR

This paper investigates how Earth's rotation influences predictions of gravitational wave strong lensing rates, revealing that it significantly reduces expected event rates for various compact binary systems.

## Contribution

It introduces the impact of Earth's rotation on lensed GW event rate predictions, which was previously neglected in models.

## Key findings

- Earth's rotation causes a non-negligible modulation of GW signals.
- Updated event rates decrease by approximately 40%, 20%, and 10% for NS-NS, BH-NS, and BH-BH systems.
- The effect must be considered for accurate future GW lensing predictions.

## Abstract

The next generation of ground-based gravitational wave (GW) detectors, e.g. the Einstein Telescope, is expected to observe a significant number of strongly lensed GW events as predicted in many previous papers. However, all these works ignored the impact of the Earth's rotation on this prediction. Multiple lensed images arrive at the Earth at different time, thus the ground-based detector has different responses to the lensed images due to different orientations of the detector relative to the GW source direction. Therefore the amplitudes of the GW signal from different images are modulated appropriately, in addition to the lensing magnification. In order to assess this effect, we performed Monte Carlo simulations to calculate the event rate of lensed GW signals. Our conclusion is that the Earth's rotation has a non-negligible impact on the event rate of lensed GW image. The updated event rates decrease by factors of $\sim40\%, \sim20\%, \sim10\%$, for NS-NS, BH-NS, BH-BH systems respectively.