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In class, the professor has tried to derive the equation by using the principle of least-action. (But not yet completed. Maybe next class...)

However I heard this method is used by Hilbert, who had derived the equation 5 days before Einstein derived it.

Then, what method did Einstein use to derive the gravitational field equation?

And why did Einstein choose to use Riemann geometry ?

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# By what method did Einstein derived his gravitational field equation?

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