Detection of extremely low frequency gravitational wave using gravitational lens

Abstract: The effect of gravitational wave of cosmological wavelength on the gravitational lensing is investigated. When the source, deflector, and observer are aligned in a highly symmetric configuration, an Einstein ring will be observed by the observer. There will be no time delays between different locations on the Einstein ring in the absence of gravitational wave. Otherwise, time delays between different locations on the Einstein ring will emerge if cosmological gravitational wave propagates through the system. Previous studies demonstrated that the time delay resulting from the aligned source-deflector-observer configuration in the presence of gravitational wave of cosmological wavelength could be equivalent to that of a similar lens with a nonaligned source-deflector-observer configuration in the absence of gravitational wave. Results in this work show that gravitational lens with the aligned source-deflector-observer configuration could serve as a potential gravitational wave detector when the whole Einstein ring observed by the observer is taken into account.