Interferometer Response to Scalar Gravitational Waves

Abstract

It was recently suggested that the magnetic component of Gravitational Waves (GWs) is relevant in the evaluation of frequency response functions of gravitational interferometers. In this paper we extend the analysis to the magnetic component of the scalar mode of GWs which arise from scalar-tensor gravity theory. In the low-frequency approximation, the response function of ground-based interferometers is calculated. The angular dependence of the electric and magnetic contributions to the response function is discussed. Finally, for an arbitrary frequency range, the proper distance between two test masses is calculated and its usefulness in the high-frequency limit for space-based interferometers is briefly considered.1

Precise response function for the magnetic component of gravitational waves in scalar-tensor gravity

“…In fact, the so-called magnetic components of GWs have to be taken into account in the context of the total response functions of interferometers for GWs propagating from arbitrary directions, [7,[40][41][42][43][44]. In a recent paper, the magnetic component has been extended to GWs arising from STG too [45]. In particular, in Ref.…”

“…In particular, in Ref. [45] it has been shown that if one neglects the magnetic contribution considering only the low-frequency approximation of the electric contribution, an important portion of the signal could be, in principle, lost in the case of STG too, in total analogy with the standard case of GTR [7,[40][41][42][43][44]. Then, it is clear that the computation of a more precise response function for the magnetic contribution is important also in the framework of the possibility of distinguishing other gravitational theories from GTR.…”

“…A GW drives the masses in the plane of the wave front and also, to a smaller extent, back and forth in the direction of the propagation of the wave. To describe this motion, the notion of electric and magnetic components of the gravitational force due to a GW can be introduced, as it has been discussed in [7,[40][41][42][43][44][45]. The analogy is not perfect, but it shows some important features of the phenomenon [40].…”

“…In Refs. [7,[40][41][42][43][44][45], the positions and motion of free test masses have been analyzed in the local inertial reference frame associated with one of the masses, i.e., the beam splitter in the case of an interferometer. It is well known that this choice of coordinate system is the closest thing to the global Lorentzian coordinates that are normally used in electrodynamics [24].…”

“…It is well known that this choice of coordinate system is the closest thing to the global Lorentzian coordinates that are normally used in electrodynamics [24]. The distinction among the electric and magnetic components of motion, as well as compared with electrodynamics, is particularly clear in this description [7,[40][41][42][43][44][45]. When one interacts with the detection of GWs, the usually used equations, with the curvature tensor in them, are only the zero-order approximation in terms of L=, where L is the length of the arms of the interferometer and the wavelength of the propagating GW [7,[40][41][42][43][44].…”