Peeling theorem

In general relativity, the peeling theorem describes the asymptotic behavior of the Weyl tensor as one goes to null infinity. Let γ be a null geodesic in a spacetime ( M , g a b ) from a point p to null infinity, with affine parameter λ . Then the theorem states that, as λ tends to infinity:

where C a b c d is the Weyl tensor, and we used the abstract index notation. Moreover, in the Petrov classification, C a b c d ( 1 ) is type N, C a b c d ( 2 ) is type III, C a b c d ( 3 ) is type II (or II-II) and C a b c d ( 4 ) is type I.