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:


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

where $$C_{abcd}$$ is the Weyl tensor, and abstract index notation is used. Moreover, in the Petrov classification, $$C^{(1)}_{abcd}$$ 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.