[musgravepeter]

The article mentions "few known exact solutions". There are actually quite a number. Most are from after 1950.

Cambridge University Press has two good books: Exact Spacetimes in Einstein's General Relativity (Griffith & Podolsky) - good readable (if you speak GR) account of the more common solutions Exact Solutions of Einstein's Feild Equations (Stephani, Kramer, MacCallum, Hoenstelaers, Herlt) - encyclopedic, authoritative and mathematical. In my case an aspirational purchase

[immmmmm]

the gr_qc list on arXiv is quite vivid, it's pretty amazing what this system of equations yields as solutions.

https://arxiv.org/archive/gr-qc