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 abstract index notation is used. 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.

References

• Wald, Robert M. (1984), General Relativity, University of Chicago Press, ISBN 0-226-87033-2