Disformal gravitational waves

TL;DR

This paper investigates how disformal transformations affect gravitational waves, providing conditions for when GWs change under such transformations and demonstrating the generation of tensorial GWs from non-linear effects.

Contribution

It establishes necessary and sufficient conditions for GW changes under disformal transformations and illustrates non-linear generation of tensorial GWs from scalar solutions.

Findings

Disformal transformations can alter GW properties depending on the frame.

A specific radiative solution maps to a disformed geometry without shear-free frames.

Non-linear effects can generate tensorial GWs overlooked in linear theory.

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.