On the Gravitational Field of a Sphere
of Incompressible Fluid
according to Einstein's Theory
by K. Schwarzschild
(Communicated February 24th, 1916 [see above p. 313].)
(Translation by S. Antoci
§1. As a further example of Einstein's theory of gravitation I have calculated the gravitational
field of a homogeneous sphere of finite radius, which consists of incompressible fluid. The addition
"of incompressible fluid" is necessary, since in the theory of relativity gravitation depends not only
on the quantity of matter, but also on its energy, and e. g. a solid body in a given state of tension
would yield a gravitation different from a fluid.
The computation is an immediate extension of my communication on the gravitational field of
a mass point (these Sitzungsberichte 1916, p. 189), that I shall quote as "Mass point" for short.
§2. Einstein's field equations of gravitation (these Sitzungsber. 1915, p. 845) read in general: