The detectability of single spinless stellar-mass black holes through gravitational lensing of gravitational waves with advanced LIGO

Abstract

We investigate the detectability of gravitational waves that have been lensed by a spinless stellar-mass black hole, with respect to the advanced LIGO. By solving the full relativistic linear wave equations in the spacetime of a Schwarzschild black hole, we find that the strong gravity can create unique signals in the lensed waveform, particularly during the merger and ringdown stages. The differences in terms of fitting factor between the lensed waveform and best-fitted unlensed general relativity template with spin-precessing and higher-order multipoles are greater than $5\%$ for the lens black hole mass within $70M_{\odot}<M_{\rm lens}<133.33 M_{\odot}$ under advanced LIGO's sensitivity. This is up to 5 times more detectable than the previous analysis based on the weak field approximation for a point mass and covers most part of the black hole mass gap predicted by stellar evolution theory. Based on Bayesian inference, the lensing feature can be distinguished with a signal-to-noise ratio of 12.5 for $M_{\rm lens}=70 M_{\odot}$ and 19.2 for $M_{\rm lens}=250 M_{\odot}$, which is attainable for advanced LIGO.