Abstract

During the years 1912-1918, the creative efforts of Albert Einstein (b. 1879 - d. 1955) were directed towards the discovery of General Relativity Theory, name under which he meant a comprehensive theory of gravito-dynamic phenomena, including principia, mathematical equations, interconnections between space, time and matter and physical implications at all scales of matter aggregation. Out of this relatively large period of scientific activity, we focused our attention to a much more restrictive period, namely the week since 18^th to 25^th November 1915, when the efforts of Einstein were for the first time successfully materialized in mathematical equations never infringed since that time on. The purpose of this paper is that to reconstitute the demonstrations left aside, for the sake of graphical space economy, in the two works published by Einstein on 18^th and 25^th November 1915 in Sitzungsberichte (Berlin). So, we hope to enlighten to a greater extent the line of reasoning which led to one of the outstanding discovery of XX-th century - the General Relativity Theory. At the same time, a historical explanation, concerning the priority of Einstein referred to other competitors, is given now, when a centennial celebration of another famous Einstein's discovery - the Special Theory of Relativity - does happen.

Conclusions

The two papers of Albert Einstein dated 18^th and 25^th November 1915 highlight a key moment for the thoughts that eventually led to the discovery of the General Relativity as a viable theory of the dynamic gravitational phenomena. Published in a lapidary form, apparently sparing graphical space, the two articles, the first with the three relativistic tests of the gravity and the second establishing the field equations, appeared in a crucial moment of crisis, when the efforts to create the gravito-dynamics based on the restricted relativity failed and the only chance was Einstein's "General Relativity". In 1914, Einstein did not know yet how he will couple the gravitational field to its sources, but in the late fall of 1915, the necessary clarification occurred to him. The equivalence principle works in the space free of sources, where the curvature scalar is zero, together with the scalar of the matter tensor. The solutions of the field in this domain should be prolonged up to the source zone where the two scalars differ from zero inasmuch as to fulfill the following purposes: (i) to result a linear relation between the tensors R_μν, T_μν and gT_μν or (equivalently) between the tensors T_μν , R_μν and gR_μν and (ii) to recover, in the non-relativistic case, the Poisson equation. In the epoch of working out the general relativity, Einstein was so much concerned with the equality of various types of motion inasmuch as he was conducted to contest the role of the inertia principle (and the corresponding Poincaré transformation group) in the enlightenment of physical theories and avoided to use the inertial frame of the observer. But precisely in this reference frame it is possible to define the mechanical Lagrangean L=-m₀cdS/dt , as well as the concept of "gravitational refractive index", standing at the ground of the discovery of the 4^th test of the general relativity theory by Irving Shapiro in 1961, namely "the retardation of a radar signal caused by passing through an intense gravitational field". However, we have to point out the fact that Einstein's attitude regarding the inertia principle changed since 1938 when, working with Hoffmann and Infeld in the many-body gravitational problem, he has been obliged to admit that the mass center moves inertially. In the controversy about the existence of black holes with finite spatial extension, Einstein adopted, likewise Schwarzschild, a negative position (that is that there exist only punctual black holes surrounded by a horizon with constant area S=16πμ², as a result of a strong deviation of the geometric manyfold from the Euclidean geometry at inter-particle distances of the order of magnitude μ=GM/c²). In the whole Einsteinean thinking, one may remark a priority of the intuition based on observation and experiment, in contrast to pure mathematical speculations, which should be subjected to a lucid control. We believe that the reconstruction of the two papers dated on November 1915, with details, thus allowing to young scientists to follow Einstein's deep physical thinking line, is most useful and instructive.