Peeling theorem

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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 we used the abstract index notation. Moreover, in the Petrov classification, C^{(1)}_{abcd} is type IV, C^{(2)}_{abcd} is type III, C^{(3)}_{abcd} is type II (or II-II) and C^{(4)}_{abcd} is type I.


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