My question arises from the interpretation of Ricci curvature. If I am not mistaken :
The Ricci scalar measures the change of volume of small geodesic balls, compared to a euclidean space, it is a generalization of the notion of Gauss curvature.
The Ricci tensor measures the change of volume of small spherical geodesic cones. So it accounts for a "directional" or "partial" change of volume of small geodesic balls in a way.
As a consequence, if the Ricci tensor is not zero, a null Ricci scalar means that geodesic balls do not change volume, but are still deformed. Like a ball becomes an ellipsoid of same volume, say.
Now if we take a Ricci-flat space with the Schwarzschild metric for example, the space outside the Schwarzschild radius is empty of matter-energy and Ricci-flat. So no change in volume nor form. But, there is still a curvature because the Riemann tensor is not zero, and the spherical mass has to curve space anyway.
Since the only non-vanishing part left of the Riemann tensor must be the Weyl tensor, most books and articles I've read attribute the space curvature to the tidal forces of gravitational waves. BUT, tidal forces would deform the geodesic balls, wouldn't they ? So there couldn't be any !
Evidently, I am missing something in the interpretation of the Weyl tensor. Is it geodesic deviation ? Can there be gravitational waves without tidal forces ?
[EDIT : My mistake was to think the deformation of geodesic balls was measured only by the Ricci tensor, when in fact both it and the Weyl tensor account for deformation, though for different reasons.]