David Hilbert originally formulated the field equations by varying the Hilbert action, while Albert Einstein derived the same equations motivated by a covariant extension of Poisson's equation for gravity. Hilbert's discovery occurred five days prior to Einstein's, although Einstein's work was influenced by the equivalence principle, which conceptualized gravity as the geometry of space-time. Consequently, the equations are attributed to Einstein, while the action is referred to as the "Hilbert action."
PREREQUISITESPhysicists, historians of science, and students of general relativity seeking to understand the origins and development of field equations in gravitational theory.
captain said:this is a question more about the history of the field equations, but did Einstein get his field equations originally by varying the Einstein-Hilbert action or was it that the field equations was were found first then the they can also be shown by the varying the action. my feeling is that its the latter but i just want be cleared about any doubts.