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

Abstract

The important issue of the magnetic component of gravitational waves (GWs) has been considered in various papers in the literature. From such analyses, it has been found that such a magnetic component becomes particularly important in the high-frequency portion of the frequency range of ground based interferometers for GWs which arises from standard general theory of relativity (GTR). Recently, such a magnetic component has been extended to GWs arising from scalar-tensor gravity (STG) too. After a review of some important issues on GWs in STG, in this paper we reanalyze the magnetic component in the framework of STG from a different point of view, by correcting an error in a previous paper and by releasing a more precise response function. In this way, we also show that if one neglects the magnetic contribution considering only the low-frequency approximation of the electric contribution, an important part of the signal could be, in principle, lost. The determination 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. At the conclusion of this paper, an expansion of the main results is also shown in order to recall the presence of the magnetic component in GTR too.

Gravito-electromagnetic analogies

“…[1,2] by one of the authors (to whom the exact GEM fields analogy of Sec. 3 was not yet known), it was suggested that the above mapping could be interpreted as arising from the similarity of magnetic tidal forces manifest in relations (132). It seems, however, to be much more related to the analogy based on GEM "vector" fields manifest in Eqs.…”

“…We start in Sec. 2 by revisiting the approach based on tidal tensors introduced in [1] (and partly reviewed in [3]), completing it by extending the formalism to the full gravitational field equations (cast herein as the Einstein field equations, plus the algebraic Bianchi identities). More precisely, through suitable projector techniques, we make a full 1+3 covariant splitting of the latter, obtaining a set of six algebraic equations: four of them involve only the sources, the "gravitoelectric" (E αβ ) and "gravitomagnetic" (H αβ ) tidal tensors, and are formally similar to the Maxwell equations written in this formalism; plus an additional pair of equations that involve the purely spatial curvature (encoded in the tensor F αβ ) and have no electromagnetic analogue.…”

The commutator algebra of covariant derivative as general framework for extended gravity. The Rastall theory case and the role of the torsion

“…In this case, labelling the metric perturbation due to the additional GW polarization as h Φ , to the first order approximation of h + , h × and h Φ , the motion of the mirror due to the GW is [57,58,60] …”

Phase space analysis of interacting dark energy in f(T) cosmology

“…Other models where matter action is modified include the bulk viscous stress [35][36][37] and the anisotropic stress [38] or some exotic fluid like Chaplygin gas (CG) [39]. One of the crucial tests to check the viability of extended theories of gravity is the potential detection of gravitational waves [40][41][42].…”