"(47)"
It can also be shown that the choice of these equations is connected with a minimum of arbitrariness. For besides Bμν, there is no tensor of the second rank, which can be built out of gμν’s and their derivatives no higher than the second, and which is also linear in them.
It will be shown that the equations arising in a purely mathematical way out of the conditions of the general relativity, together with equations (46), give us the Newtonian law of attraction as a first approximation, and lead in the second approximation to the explanation of the perihelion-motion of mercury discovered by Leverrier (the residual effect which could not be accounted for by the consideration of all sorts of disturbing factors). My view is that these are convincing proofs of the physical correctness of my theory.
§15. Hamiltonian Function for the Gravitation-field.
Laws of Impulse and Energy.
In order to show that the field equations correspond to the laws of impulse and energy, it is most convenient to write it in the following Hamiltonian form:—
(47a)
δ∫ Hdτ = 0
H = gμν γαμβ γβνα
√(-g) = 1