Vankov, Anatoli Andrei
August 04, 2014
Einstein, Schwarzschild, General Relativity, Mercury perihelion, ﬁeld equations.
Einstein’s original paper “Explanation of the Perihelion Motion of Mercury from General Relativity Theory”, 1915, published in German and decades later translated into English, remains hardly accessible for readers. We present the translation recently made by Professor Roger Rydin from the University of Virginia who paid much attention to lin- guistic ﬁdelity and scientiﬁc adequacy of the texts. It is followed with our critical Comments concerning the rigor of Einstein’s derivation of the equation of motion and the corresponding approximate solution leading to the perihelion advance formula. The latter was obtained in numerous works later on from the Schwarzschild “exact” solution. Schwarzschild presented it ﬁrstly in his letter to Einstein and claimed the formula derived from his solution “identical” to Einstein’s one. We draw readers’ attention to the fact, however, that some parameters in the Schwarzschild’s formula have diﬀerent physical meanings. This makes formulas, though formally similar, not identical. Yet, one can directly verify that, no matter how the equation is derived, its widely claimed “approximate solution” does not ﬁt the equation.