The newtonian limit for general relativity exists only for the asymptotically flat spacetimes.(adsbygoogle = window.adsbygoogle || []).push({});

FRW case definitely not asymptotically flat. SO the newtonian limit should not exist for it.

However we have Newtonian theory of cosmology in homogeneous and isotropic universe.

So my question is is it possible to obtain Newtonian cosmology from taking appropriately defined limit of FRW cosmology???

Secondly if we consider for instance Oppenheiner-Sneider collapse.

Collapse of the star which remains spatially homogeneous.

In this case The metric inside star is given by FRW. Outside it`s given by schwarzschild metric.

Hence this situation is asymptotically flat. So newtonian limit would make sence in this case.

If we try to take limit inside star

metric is given by

(ds)**2 = -(dt)**2+ space part

we need to compare that with

(ds)**2 = -(1+2*Phi)(dt)**2+ space part

where Phi is newtonian gravitational potential

compare these two

it implies that

PHi=0

hence essentially no gravity inside the star.

This is clearly not right..

Since there would be gravity inside star in Newtonian limit.

So where lies fault in the above argument??

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# Newtonian limit FRW

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