Peeling theorem

In general relativity, the peeling theorem describes the asymptotic behavior of the Weyl tensor as one goes to null infinity. Let $\gamma$ be a null geodesic in a spacetime $(M,g_{{ab}})$ from a point p to null infinity, with affine parameter $\lambda$ . Then the theorem states that, as $\lambda$ tends to infinity:

C_{{abcd}}={\frac {C_{{abcd}}^{{(1)}}}{\lambda }}+{\frac {C_{{abcd}}^{{(2)}}}{\lambda ^{2}}}+{\frac {C_{{abcd}}^{{(3)}}}{\lambda ^{3}}}+{\frac {C_{{abcd}}^{{(4)}}}{\lambda ^{4}}}+O\left({\frac {1}{\lambda ^{5}}}\right)

where $C_{{abcd}}$ is the Weyl tensor, and we used the abstract index notation. Moreover, in the Petrov classification, $C_{{abcd}}^{{(1)}}$ is type N, $C_{{abcd}}^{{(2)}}$ is type III, $C_{{abcd}}^{{(3)}}$ is type II (or II-II) and $C_{{abcd}}^{{(4)}}$ is type I.

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