How were the Hilbert – Einstein equations discovered?

Abstract

The pathways along which A. Einstein and D. Hilbert independently came to the gravitational field equations are traced. Some of the papers that assert a point of view on the history of the derivation of the gravitational field equations "that radically differs from the standard point of view" are critically analyzed. It is shown that the conclusions drawn in these papers are completely groundless.

The Electromagnetic Conception of Nature at the Root of the Special and General Relativity Theories and its Revolutionary Meaning

“…The more important differences concern the general covariance of the theory-not completely satisfied in the draft (there were, beyond the ten general covariant equations, four other non general covariant ones to guarantee the validity of the causality and energymomentum conservation principles) as well as in previous works by Einstein-and the ''non-explicit'' form of the field equations: the gravitational part of field equations was given by the variation derivative of the gravitational term HgK in respect to the metrics g lm , but this derivative does not appear to have been calculated by Hilbert in the part of the draft that has been discovered (Renn and Stachel 1999; Logunov et al 2004). …”

“…Other criticisms of Corry-Renn-Stachel's work seem to me very relevant: beyond mathematical argumentations, it is important to take account of the fact that the Hilbert draft is incomplete, with gaps (Logunov et al 2004).…”

A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit

“…In the special case of perturbations around an spherically symmetric background, as the Schwarzschild one with mass M, we can benefit from the decomposition into spherical harmonics (labeled by ℓ, m) of the metric and hence obtain a set of HilbertEinstein [17,37] field equations for metric coefficients depending only on time and radial coordinates, i.e. the Schwarzschild's (t, r).…”