Does the Ricci tensor actually change volume of a body in reality? I have learned about the Ricci tensor and I was wondering if it actually changes volume in real-life physics.

The question
I know the Ricci tensor is a mathematical object but does it only change the volume of an object along geodesics in a mathematical sense (not related to reality) or in an actual physical sense (reality) like in the tidal forces of gravity?

If it does change volume in reality, how does it? I mean, if a body has a constant amount of mass, how can the body's volume increase/decrease?
And can you provide which fields/spaces (examples) would the volume increase or decrease?
Please note: I am quite new to General Relativity and have not learned the Einstein field equations yet.
 A: I believe you are talking about the notions of geodesic congruence and the Raychaudhuri's equation, which are closely related to the Ricci tensor. Families of nearby geodesics diverge in negatively curved space and converge in positively curved space. They can also exhibit shear and vorticity.
Keep in mind that volume = density / mass and the mass will not change, though the volume and density may. Of course, for some objects the density will not change either. In this case the particles in the object are not actually following geodesics, because there are internal forces which act on them.
A: Gravitational wave detectors work by measuring tiny differences in the length of the path of laser beams caused by ripples in space-time. So yes, curvature can change the length of a path and the volume of a region.
For example, imagine a box in free-fall above the surface of the earth. For simplicity, imagine it is going along a path straight toward the earth's center (falling straight down). If each corner of the box travels along its geodesic (its natural path through space-time), the corners of the box will be drawn closer together as they each travel toward the center of the earth. Now, if there are electromagnetic forces forcing the box to hold its shape, the box may not change in volume. It will, however, feel the force of compression, and that force will have to be balanced out by some other force or the box will contract. If you just have a free falling laser and mirror setup, the time it takes to the laser light to bounce off the mirror and arrive back at the laser will be shorter in the gravitational field than in flat space.
A: The Ricci tensor does indicate a physical change in volume for a momentarily comoving set of non-interacting particles. Think of a cloud of dust, not a solid object. As the cloud of dust collapses the distance between particles reduces.
For a solid object the volume will not decrease as indicated, but there will be some internal stresses produced.
