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Albert Einstein's discovery of the gravitational field equations of general relativity and David Hilbert's almost simultaneous derivation of the theory using an elegant variational principle, [B 1]: 170 during a period when the two corresponded frequently, has led to numerous historical analyses of their interaction.
In his 1982 Einstein biography Subtle is the Lord, [B 3] Abraham Pais argued that Poincaré "comes near" to discovering special relativity (in his St. Louis lecture of September 1904, and the June 1905 paper), but eventually he failed, because in 1904 and also later in 1909, Poincaré treated length contraction as a third independent hypothesis ...
[h] Nearly simultaneously, Hilbert published "The Foundations of Physics", an axiomatic derivation of the field equations (see Einstein–Hilbert action). Hilbert fully credited Einstein as the originator of the theory and no public priority dispute concerning the field equations ever arose between the two men during their lives.
The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the (− + + +) metric signature , the gravitational part of the action is given as [ 1 ]
1915 – David Hilbert independently introduces the Einstein-Hilbert action. [59] [56] Hilbert also recognizes the connection between the Einstein equations and the Gauss-Bonnet theorem. [60] 1916 – Karl Schwarzschild publishes the Schwarzschild metric about a month after Einstein published his general theory of relativity.
The differences between Einstein–Cartan theory and general relativity (formulated either in terms of the Einstein–Hilbert action on Riemannian geometry or the Palatini action on Riemann–Cartan geometry) rest solely on what happens to the geometry inside matter sources. That is: "torsion does not propagate".
It is much more restrictive than the Einstein equivalence principle. Like the Einstein equivalence principle, the strong equivalence principle requires gravity to be geometrical by nature, but in addition it forbids any extra fields, so the metric alone determines all of the effects of gravity. If an observer measures a patch of space to be ...
The Einstein–Hilbert action for general relativity was first formulated purely in terms of the space-time metric. To take the metric and affine connection as independent variables in the action principle was first considered by Palatini. [1]