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haushofer

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This has a nice piece of history :)

David Hilbert first found the field equations, by varying his action. Einstein found the same equations, but his motivation was a covariant extension of Poisson's equation for the gravitational field. I believe that Hilbert found the field equations 5 days earlier than Einstein did, but he was influenced by Einstein's equivalence principe which led to the idea of gravity as space-time geometry. So the equations are rightly named after Einstein, whereas the action is called the "Hilbert action".