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When we are in truly empty space, there's no Ricci curvature, so actually our ball of coffee grounds doesn't change volume. But there can be Weyl curvature due to gravitational waves, tidal forces, and the like. Gravitational waves and tidal forces tend to stretch things out in one direction while squashing them in the other. So these would correspond to our ball changing into an ellipsoid! Just as we hoped. Similarly, when a ball of coffee grounds falls freely through outer space in the earth's gravitational field, it feels no Ricci curvature, only Weyl curvature. So the "tidal forces" due to some coffee grounds being near to the earth than others may stretch the ball into an ellipsoid, but not change its volume.

To get the Weyl tensor, you need to know about the background fields that would be present without your sources of gravity.

when a ball of coffee grounds falls freely through outer space in the earth's gravitational field, it feels no Ricci curvature, only Weyl curvature. So the "tidal forces" due to some coffee grounds being near to the earth than others may stretch the ball into an ellipsoid, but not change its volume.

The Weyl curvature effectively measures the tidal effect. What is the ‘tidal’ effect?Recall that, from the astronaut’s point of view, it seems that gravity has been abolished but that is not quite true.Imagine that the astronaut is surrounded by a sphere of particles. Which are initially at rest with respect to the astronaut. Now, initially they will just hover there but soon they will start to accelerate because of the slight differences in the gravitational attraction of the Earth at different points on the sphere. (Notice that I am describing the effect in Newtonian language, but that is quite adequate.) these slight differences cause the original sphere of particles to become distorted into an elliptical arrangement,