Disformal gravitational waves
Abstract
Contrary to conformal transformations, disformal transformations can change the principal null directions of a spacetime geometry. Thus, depending on the frame a gravitational wave (GW) detector minimally couples to, the properties of GWs may change under a disformal transformation. In this paper, we provide necessary and sufficient conditions which determine whether GWs change under disformal transformations or not. Our argument is coordinate-independent and can be applied to any spacetime geometry at the fully non-linear level. As an example, we show that an exact radiative solution of massless Einstein-scalar gravity which admits only shear-free parallel transported frame is mapped to a disformed geometry which does not possess any shear-free parallel transported frame. This radiative geometry and its disformed counterpart provide a concrete example of the possibility to generate tensorial GWs from a disformal transformation at the fully non-linear level. This type of non-linear effect can be completely overlooked in the usual linear perturbation theory.
Cite
@article{arxiv.2402.01487,
title = {Disformal gravitational waves},
author = {Jibril Ben Achour and Mohammad Ali Gorji and Hugo Roussille},
journal= {arXiv preprint arXiv:2402.01487},
year = {2025}
}
Comments
12 pages, 1 figure, version published in JCAP