Peeling theorem

In general relativity, the peeling theorem describes the asymptotic behavior of the Weyl tensor as one goes to [http://en.wiktionary.org/wiki/null_infinity null infinity]. Let $\backslash gamma$ be a null geodesic in a spacetime $(M,\; g\_\{ab\})$ from a point p to null infinity, with affine parameter $\backslash lambda$. Then the theorem states that, as $\backslash lambda$ tends to infinity:

:$C\_\{abcd\}\; =\; \backslash frac\{C^\{(1)\}\_\{abcd\}\}\{\backslash lambda\}+\backslash frac\{C^\{(2)\}\_\{abcd\}\}\{\backslash lambda^2\}+\backslash frac\{C^\{(3)\}\_\{abcd\}\}\{\backslash lambda^3\}+\backslash frac\{C^\{(4)\}\_\{abcd\}\}\{\backslash lambda^4\}+O\backslash left(\backslash frac\{1\}\{\backslash lambda^5\}\backslash right)$

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