In general relativity, the peeling theorem describes the asymptotic behavior of the Weyl tensor as one goes to null infinity. Let γ {\displaystyle \gamma } be a null geodesic in a spacetime ( M , g a b ) {\displaystyle (M,g_{ab})} from a point p to null infinity, with affine parameter λ {\displaystyle \lambda } . Then the theorem states that, as λ {\displaystyle \lambda } tends to infinity:

C a b c d = C a b c d ( 1 ) λ + C a b c d ( 2 ) λ 2 + C a b c d ( 3 ) λ 3 + C a b c d ( 4 ) λ 4 + O ( 1 λ 5 ) {\displaystyle 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 a b c d {\displaystyle C_{abcd}} is the Weyl tensor, and abstract index notation is used. Moreover, in the Petrov classification, C a b c d ( 1 ) {\displaystyle C_{abcd}^{(1)}} is type N, C a b c d ( 2 ) {\displaystyle C_{abcd}^{(2)}} is type III, C a b c d ( 3 ) {\displaystyle C_{abcd}^{(3)}} is type II (or II-II) and C a b c d ( 4 ) {\displaystyle C_{abcd}^{(4)}} is type I.

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