1. Is it already known fact that applying simple coordinate transform to de Sitter metic one can arrive to the FLRW metric with flat cosmology (k=0)?
2.Is such transform just coincidence or has significance?
Many thanks..
k=0 isn't flat cosmology-it implies that the spatial part is flat.
Cf. for example, https://www.ast.cam.ac.uk/~pettini/Intro%20Cosmology/Lecture03.pdf for a review. This isn't new.
Stam, thank you for your response! Yes, I meant k=0 & spatial part is flat. I see the connection in your reference, but presented via different approach...
If this fact is not new then why the correspondence of the Schwarzschild-de Sitter to the FLRW with central gravity is not such obvious problem? I red that Einstein tried to solve it, Gilbert and McVittie and there are still debates on this nowadays..
That's just history. This has now been resolved-just read the lectures linked to; more details can be found here: Article Lecture Notes on General Relativity
or https://kpfu.ru/portal/docs/F1110497646/Starobinsky.pdf
What's ``obvious'' and what isn't doesn't mean anything-it's personal opinion, not a technical, impersonal, statement. What matters is that the mathematical procedure is, now, well understood, so it's better to skip history and focus on the technical aspects.
Section 8 has nice explanation on the correspondence of the FLRW to de Sitter for isotropic and homogeneous Universe. But there is no single word on the FLRW with central gravity (FLRW + Schwarzschild).
Probably it should be in the Section 9 of the book but the Section is missing)
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