Exact Solutions in General Relativity
Caption: A cartoon of a Schwarzschild black hole (FK-545; ABS-195,222). A Schwarzschild black hole is a spectial case of the Schwarzschild solution, an exact (analytic) solution in general relativity. For further explication of the image, see Black hole file: black_hole_schwarzschild_cartoon.html.Exact solutions in general relativity explicated:
- Defining an
exact (analytic) solution
in general relativity
(i.e., for physical systems)
is a bit tricky and so is counting exact solutions
since many are special cases of others.
- By one expert's count, there are,
circa 2022, only
6 top-level
(i.e., general and important) exact solutions in general relativity (see M.A.H. MacCallum, 2013,
Exact solutions of Einstein's equations).
There are many special cases of the 6 top-level exact solutions in general relativity.
- Long ago in the 1990s,
yours truly vaguely recalls a
Russian speaker who was
introduced as having discovered 2
of the
6 top-level
exact solutions in general relativity.
- To the knowledge of yours truly,
Albert Einstein (1879--1955) himself
found only one exact solution---the
Einstein universe
in field of
cosmology---which
is taken up in IAL 30: Cosmology.
And it is NOT one of the
6 top-level
exact solutions in general relativity.
The Einstein universe is a special case of the
Friedmann-Lemaitre-Robertson-Walker solution
in the count of
M.A.H. MacCallum (2013).
- Finding new exact solutions
in general relativity is always hard work
and it gets harder with time since only harder ones are left to be found.
Image link: Itself.
Local file: local link: general_relativity_exact_solutions.html.
File: Relativity file: general_relativity_exact_solutions.html.