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I've been reading about Petrov classification and I have a question (in fact this is an exercise from Wald's General Relativity): How can we prove that spherically symmetric spacetimes are algebraically special, using the fact that the Weyl tensor, as the principal null directions are invariant over isometries? I've look over the internet, but I coudn't find a clue.

Thanks for any help!

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# On Petrov classification

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