Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story

TL;DR

This paper discusses the development of Einstein's general relativity theory, highlighting Schwarzschild's exact solution to Einstein's field equations and its significance in explaining Mercury's perihelion motion.

Contribution

It presents the historical and scientific context of Schwarzschild's exact solution and its relation to Einstein's approximate solutions in general relativity.

Findings

Schwarzschild derived the first exact solution to Einstein's field equations.

Schwarzschild's solution explained Mercury's perihelion motion.

Einstein acknowledged Schwarzschild's exact solution in his 1916 review.

Abstract

On November 18, 1915 Einstein reported to the Prussian Academy that the perihelion motion of Mercury is explained by his new General Theory of Relativity: Einstein found approximate solutions to his November 11, 1915 field equations. Einstein's field equations cannot be solved in the general case, but can be solved in particular situations. The first to offer such an exact solution was Karl Schwarzschild. Schwarzschild found one line element, which satisfied the conditions imposed by Einstein on the gravitational field of the sun, as well as Einstein's field equations from the November 18, 1915 paper. On December 22, 1915 Schwarzschild told Einstein that he reworked the calculation in his November 18 1915 paper of the Mercury perihelion. Subsequently Schwarzschild sent Einstein a manuscript, in which he derived his exact solution of Einstein's field equations. On January 13, 1916, Einstein delivered Schwarzschild's paper before the Prussian Academy, and a month later the paper was published. In March 1916 Einstein submitted to the Annalen der Physik a review article on the general theory of relativity. The paper was published two months later, in May 1916. The 1916 review article was written after Schwarzschild had found the complete exact solution to Einstein's November 18, 1915 field equations. Einstein preferred in his 1916 paper to write his November 18, 1915 approximate solution upon Schwarzschild exact solution (and coordinate singularity therein).