Cosmological models with metrics and curvature tensors

[tom.stoer]

Does anybody know about a comprehensive list of cosmological models and their properties? E.g. FRW, dS, AdS, ... Goedelspacetime, ... with metrics g, Christoffel symbols, Riemann tensors, Ricci, Ricci scalar, Kretschmann scalar, ...

Tom

 

[Mentz114]

That's a big ask. I've never seen a book or paper that lists all that stuff for every metric. The comparison papers which summarize models tend to focus on symmetries and invariants. There's a good slice of that in this paper arXiv:gr-qc/0004016v1 (Bicak) and in 'the book', "Exact Solutions of Einstein's Field equations", Stephani et al (2nd edition).

You could get GrTensor or Maxima and calculate them yourself from the metrics.