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I have a question concerning the Wald's book: General Relativity.

In the appendix E, he derived the Einstein equation by considering the surface term (GHY).

I do not understand what he said after the equation (E.1.38).

Actually he considers that [itex]h^{bc}\nabla_c(\delta g_{ab})=0[/itex], because we fix [itex]\delta g_{ab}=0[/itex] on the surface, but therefore why the other term in (E.1.38) is not null, the term [itex]h^{bc}\nabla_a(\delta g_{bc})[/itex].

They look the same for me, and after some algebra, where we replace the covariant derivative by the one compatible with the metric on the surface we should have a total derivative term on the surface that we can integrate away.

Thanks in advance

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# Clarification on Wald's book

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