Gravitational grating

Abstract

In this work, we study the interaction of the electromagnetic wave (EW) from a distant quasar with the gravitational wave (GW) sourced by the binary stars. While in the regime of geometric optics, the light bending due to this interaction is negligible, we show that the phase shifting on the wavefront of an EW can produce the diffraction pattern on the observer plane. The diffraction of the light (with the wavelength of λ e ) by the gravitational wave playing the role of gravitational grating (with the wavelength of λ g ) has the diffraction angle of ∆β ∼ λ e /λ g . The relative motion of the observer, the source of gravitational wave and the quasar results in a relative motion of the observer through the interference pattern on the observer plane. The consequence of this fringe crossing is the modulation in the light curve of a quasar with the period of few hours in the microwave wavelength. The optical depth for the observation of this phenomenon for a Quasar with the multiple images strongly lensed by a galaxy where the light trajectory of some of the images crosses the lensing galaxy is τ 0.2. By shifting the time-delay of the light curves of the multiple images in a strong lensed quasar and removing the intrinsic variations of a quasar, our desired signals, as a new method for detection of GWs can be detected.

Gravitational lensing beyond geometric optics: I. Formalism and observables

“…This can be solved by introducing an affine distance r which satisfies (16). If A 1 and A ′ 1 are assumed to coincide on a hypersurface r = r 0 , where k • ∇r 0 = 0,…”

“…While the basic equations governing geometric optics and its corrections have been discussed elsewhere [10,11,12] from a general spacetime perspective, very few of their higher-order consequences appear to have been explored. Some discussions which do go beyond geometric optics have appeared in various contexts, although most of these have employed a different "pseudo-Euclidean" approach which is restricted to weakly-curved spacetimes [1,13,14,15,16].…”

Propagation of electromagnetic waves in MOG: gravitational lensing

“…We impose the Lorenz gauge condition ∇µA µ = 0 and for empty space, we omit the third term on the left-hand side of equation (26). The expression for ∇ µ ∇µA i in terms of partial derivatives with respect to A µ and perturbations of the metric is derived in (Rahvar 2018) as follows:…”

“…The expression for ∇ µ ∇µA i in terms of partial derivatives with respect to A µ and perturbations of the metric is derived in (Rahvar 2018) as follows:…”

“…There is a standard approach in wave optics to derive the lensing equation by considering the interference of the light rays received by the observer at the screen S. We can calculate the geometric limit for λe → 0. Also, the trajectory of light in geometric optics is obtained from Fermat's potential (Schneider et al 1992;Nakamura& Deguchi 1999 ;Rahvar 2018). Let us define Fermat's potential as the overall phase of a light ray from the source to the observer.…”