Kinematical Description
Describing the mutual motion of the test particles in a null geodesic congruence in a spacetime such as the Schwarzschild vacuum or FRW dust is a very important problem in general relativity. It is solved by defining certain kinematical quantities which completely describe how the integral curves in a congruence may converge (diverge) or twist about one another.
It should be stressed that the kinematical decomposition we are about to describe is pure mathematics valid for any Lorentzian manifold. However, the physical interpretation in terms of test particles and tidal accelerations (for timelike geodesic congruences) or pencils of light rays (for null geodesic congruences) is valid only for general relativity (similar interpretations may be valid in closely related theories).
Read more about this topic: Congruence (general Relativity)
Famous quotes containing the word description:
“To give an accurate description of what has never occurred is not merely the proper occupation of the historian, but the inalienable privilege of any man of parts and culture.”
—Oscar Wilde (1854–1900)