Why is the Hilbert Action and the matter actionof the Einstein's Gravitation theory diffeomorphism invariant, as Wald said in his textbook General Relativity on Page 456 and Sean Carroll said in his Spacetime and Geometry on Page 435.(adsbygoogle = window.adsbygoogle || []).push({});

In other words，why do we have to set

[tex]\delta S_{M}[/tex] to be zero?

Thx!

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# The Hilbert Action

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