The Continuity Between Classical and Relativistic Cosmology in the Work of Karl Schwarzschild

Abstract

Only a few weeks after Einstein had presented the successful calculation of Mercury’s perihelion advance on the basis of his new theory of general relativity in late 1915, the German astronomer Karl Schwarzschild (1873–1916) published the first non-trivial exact solution of Einstein’s field equations (Schwarzschild 1916a). The solution describes the spherically symmetric gravitational field in a vacuum and holds a central place in gravitation theory, comparable to that of the Coulomb potential in electrodynamics. It was not only an important point of departure for further theoretical research but also, up to recent times, the basis for all empirical tests of general relativity that proved not only the principle of equivalence but also the field equations themselves. Schwarzschild made a further substantial contribution to the theory when he found another exact solution describing the interior gravitational field of a sphere of fluid with uniform energy density (Schwarzschild 1916b). In this communication an important quantity makes its first appearance. It is the quantity that is later known as the Schwarzschild radius , which plays an important role in the theory of black holes many decades later. 1 But even long before the final theory of general relativity was established, Schwarzschild had already occupied himself with possible implications of its predecessors for astronomy; in 1913 he carried out observations of the solar spectrum in order to clarify if the gravitational redshift predicted by Einstein on the basis of the equivalence principle was detectable (Schwarzschild 1914). In view of the fundamental role played by general relativity in astronomy, astrophysics, and cosmology today, it appears quite natural that an astronomer would engage in the study of this theory. Astronomical objects of all scales ranging from supermassive stars via galaxy nuclei and quasars to the universe as a whole are described on its basis. However, at the time when Schwarzschild made his contributions, the situation was quite different. None of the spectacular objects nowadays so successfully described by general relativity were in the focus of research, most of