Features:
As far as yours truly knows, Albert Einstein (1879--1955) himself only ever found only one exact analytic solution (the Einstein universe) and it is only a special case of one of the 6 general solutions: i.e., the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution.
An exact analytic solution is a solution which can be expressed as formulae you can just write down and has NO approximations
Note
Schwarzschild did NOT
use the term
black hole which was coined
in the 1960s.
For the coinage, see
Astronomer file:
ann_ewing.html.
However, Schwarzschild
did NOT have a lot of time to think about the meaning
of black holes.
He
found his eponymous
exact analytic solution
while serving
in the Imperial German Army
in 1915
at the Russian front.
He was soon invalided out of active duty by a rare
autoimmune disease and died
in 1916.
Schwarzschild was such a brilliant
general relativist that it plausible to
think that he would have anticipated some of the
general-relativity results of others
if he had lived longer: e.g., some of the early cosmological models that fall into the class of
the Friedmann-Lemaitre-Robertson-Walker (FLRW) models.