Past exam of the general relativity course of the University of Oxford / 2021 / 2 / d / iv / Solution

Gravitational waves also exhibit diffraction: the geometrical optics ray description fails when a propagation structure or lens delay is not large compared with the wave's wavelength or period. For a compact lens of mass $M_L$, a useful dimensionless parameter is $w=4G{M}_L{\omega }_{\mathrm{gw}}/c^3$; $w$ of order one signals potentially appreciable wave effects, with cosmological lens redshift supplying an additional factor $1+z_L$ when needed. Astrophysical gravitational lensing can therefore produce diffraction and frequency-dependent amplification. Ordinary objects are poor opaque screens for gravitational waves, so everyday slit-and-screen demonstrations are implausible despite the large wavelengths, which are about $3000$ km at $100$ Hz.