  This paper discusses the gauge issue touching the gravitational waves induced
at the second order by the scalar modes of cosmological perturbations. These
waves are known to depend on the gauge used for their calculation. In this
paper, we propose a simple method of obtaining physically meaningful
expressions for such scalar-induced gravitational waves at the leading order.
The method is centred on well-defined observables, such as the magnetic part of
the Weyl tensor, or the Cotton tensor of a slicing of spacetime, which vanish
in the background and do not depend linearly on the scalar perturbations.
Generalizing the Stewart-Walker lemma, it is shown that the gravitational waves
contributing to such observables at the second order are automatically
gauge-invariant, even when the observable itself does not vanish at the first
order. In each case, the scalar-induced gravitational waves are related to the
ones computed in the Newtonian gauge, first for a general background, and then
for the particular case of a spacetime dominated by either radiation or cold
matter.
