Gravitational-wave lensing and frequency fringes
Start with what a detector hears when a chirp passes a mass on two sides. Then derive the arrival time across the lens plane, the exact point-lens amplification and the test a search uses to tell a lensed chirp from an ordinary one. A reproducible tutorial and a paper guide close the course.
L1 · Concept
What a detector hears when one chirp takes two paths
A mass near the line of sight splits a gravitational-wave chirp into two delayed copies whose sum swells and fades across frequency.
L1 · Chapter
Why a lens delays a gravitational wave
Build the arrival-time surface of a point-mass lens, find its two images and their delay, and see when a wavelength is too long to split.
L2 · Chapter
The exact amplification factor of a point-mass lens
Derive the diffraction integral for a point mass, its closed form, the two-image limit at high frequency and the smooth limit at low frequency.
L3 · Chapter
Can a detector tell a lensed chirp from an ordinary one?
Weight two chirps by detector noise, compute their match and estimate how loud a signal must be before a lens shows in the fit.
L3 · Method
Recompute point-lens amplification and test a lens search
Check the closed-form amplification with an independent Fresnel integral, then inject lensed and unlensed chirps into synthetic noise.
L4 · Paper guide
How to read the O3 search for lensed gravitational waves
Read the LIGO-Virgo-KAGRA O3 lensing search for microlensing beats, image pairs and noise that imitates a lens, figure by figure.