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cianfa72

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- About the Wald's proof of existence of synchronous reference frame in a finite region of any spacetime

Hi, on Wald's book on GR there is a claim at pag. 43 about the construction of synchronous reference frame (i.e. Gaussian coordinate chart) in a finite region of any spacetime. In particular he says: $$n^b\nabla_b (n_aX^a)=n_aX^b\nabla_b \, n^a$$Then he claims from Leibnitz rule the above equals to $$\frac 1 2 X^b\nabla_b (n^an_a)$$ Why the above is true? Thanks.

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