// Workers AI · dad joke modeWhat did peeling theorem say to the banana? You're always stripping away layers.

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