Editorial note to: Ludwig Flamm, Contributions to Einstein’s theory of gravitation

Abstract

In 1916, shortly after Einstein’s paper [1] of November 18th of the previous year, there appeared in the Sitzungsberichte der Koniglich Preussischen Akademie der Wissenschaften two remarkable papers by Karl Schwarzschild. The first, in which he derived the static spherically symmetric so-called exterior vacuum solution [2] was submitted on January 13. In the second (submitted on February 24) Schwarzschild obtains the so-called interior [3] solution for a static spherically symmetric incompressible fluid ball according to General Relativity. On 3rd September of the same year Ludwig Flamm submitted the paper under current consideration [4] to the Zeitschrift fur Physik. Flamm’s aim was to render the conclusions of Einstein and Schwarzschild clearer, more transparent and, in particular those relating to photon orbits, more accurate. Flamm starts in Section 1 by recalling Schwarschild’s observation that the spatial sections of the interior solution have the geometry of a portion of a round three sphere and in his Fig. 1, he illustrates this by means of a sketch of any planar section, e.g. for θ = π2 . In Section 2 Flamm goes on to consider a planar section of the exterior solution and shows that it, like the sphere, is isometric to a surface of revolution but now the meridional curve is a parabola. Hence, by contrast with the interior case any