Peeling theorem

Peeling theorem In general relativity, the peeling theorem describes the asymptotic behavior of the Weyl tensor as one goes to null infinity. Let {displaystyle gamma } be a null geodesic in a spacetime {displaystyle (M,g_{ab})} from a point p to null infinity, with affine parameter {displaystyle lambda } . Then the theorem states that, as {displaystyle lambda } tends to infinity: {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}}}+Oleft({frac {1}{lambda ^{5}}}right)} where {displaystyle C_{abcd}} is the Weyl tensor, and we used the abstract index notation. Moreover, in the Petrov classification, {displaystyle C_{abcd}^{(1)}} is type N, {displaystyle C_{abcd}^{(2)}} is type III, {displaystyle C_{abcd}^{(3)}} is type II (or II-II) and {displaystyle C_{abcd}^{(4)}} is type I.

References Wald, Robert M. (1984), General Relativity, University of Chicago Press, ISBN 0-226-87033-2 External links [1] [2] [3] [4] This differential geometry related article is a stub. You can help Wikipedia by expanding it.

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