For a congruence of observers (or particles or photons) with four velocity , the kinematic invariants fully describe
their relative motion. Consider those that, in a particular moment , occupy the surface of an infinitesimally small sphere.
Now, consider the deformation of that surface at a later moment . The volume change is called
expansion. The shear tensor measures the ellipsoidal distortion of this sphere, and the vorticity tensor describes
its rotation (i.e., three independent rotations around three perpendicular axes). Expansion, shear, and vorticity are determined
by the tensor in the following way: , , and
. Here is the projection tensor. The acceleration is also considered
a kinematic invariant.