Exact Solutions in General Relativity

Exact solutions in general relativity explicated:

1. An exact (analytic) solution is a mathematical solution which is just a formula that is exact answer to a problem.

   In physics, exact solutions are only available for systems that are to at least some degree idealized. Nevertheless, exact solutions are all-important solving the essence of systems and in giving understanding.

   Usually for full realism, numerical solutions have to be determined by the computer.

2. 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.

3. 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.

4. 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.

5. 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).

6. 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.