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 IV, $C_{{abcd}}^{{(2)}}$ 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

External links