for the orthogonal group , and thus the Ricci decomposition is a special case of the splitting of a module for a semisimple Lie group into its irreducible factors. In dimension 4, the Weyl module decomposes further into a pair of irreducible factors for the special orthogonal group: the self-dual and antiself-dual parts W+ and W−. Physical interpretation The Ricci decomposition can be interpreted physically in Einstein's theory of general relativity, where it is sometimes called the Géhéniau-Debever decomposition. In this theory, the Einstein field equation where is the stress–energy tensor describing the amount and motion of all matter and all nongravitational field energy and momentum, states that the Ricci tensor—or equivalently, the Einstein tensor—represents that part of the gravitational field which is due to the immediate presence of nongravitational energy and momentum. The Weyl tensor represents the part of the gravitational field which can propagate as a gravitational wave through a region containing no matter or nongravitational fields. Regions of spacetime in which the Weyl tensor vanishes contain no gravitational radiation and are also conformally flat. See also Bel decomposition of the Riemann tensor Conformal geometry Petrov classification Plebanski tensor Ricci calculus Schouten tensor Trace-free Ricci tensor References . . Section 6.1 discusses the decomposition. Versions of the decomposition also enter into the discussion of conformal and projective geometries, in chapters 7 and 8. . Differential geometry Riemannian geometry Tensors in general relativity