On Arrival Time Difference Between Lensed Gravitational Waves and Light

Abstract

It is known that geometrical optics no longer applies to gravitational lensing if the wavelength of a propagating wave becomes comparable to or larger than the Schwarzschild radius of a lensing object. We investigate the propagation of gravitational waves in wave optics, particularly focusing on the difference between their arrival time and the arrival time of light. We argue that, contrary to the observation in the previous work, gravitational waves never arrive at an observer earlier than light when both gravitational waves and light are emitted from a same source simultaneously.