Astronomy and Astrophysics – Astrophysics
Scientific paper
May 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011ap%26ss.333..351m&link_type=abstract
Astrophysics and Space Science, Volume 333, Issue 1, pp.351-356
Astronomy and Astrophysics
Astrophysics
General Relativity, Gravitational Collapse, Cosmology, Friedmann-Robertson-Walker Spacetime, Big-Bang Model
Scientific paper
We consider a spherically symmetric general relativistic perfect fluid in its comoving frame. It is found that, by integrating the local energy momentum conservation equation, a general form of g 00 can be obtained. During this study, we get a cue that an adiabatically evolving uniform density isolated sphere having ρ( r, t)= ρ 0( t), should comprise "dust" having p 0( t)=0; as recently suggested by Durgapal and Fuloria (J. Mod. Phys. 1:143, 2010) In fact, we offer here an independent proof to this effect. But much more importantly, we find that for the homogeneous and isotropic Friedmann-Robertson-Walker (FRW) metric having p( r, t)= p 0( t) and ρ( r, t)= ρ 0( t), g_{00} = e^{-2p0/(p0 +ρ0)}. But in general relativity (GR), one can choose an arbitrary t→ t ∗= f( t) without any loss of generality, and thus set g 00( t ∗)=1. And since pressure is a scalar, this implies that p 0( t ∗)= p 0( t)=0 in the Big-Bang model based on the FRW metric. This result gets confirmed by the fact the homogeneous dust metric having p( r, t)= p 0( t)=0 and ρ( r, t)= ρ 0( t) and the FRW metric are exactly identical. In other words, both the cases correspond to the same Einstein tensor Gab because they intrinsically have the same energy momentum tensor Tab=operatorname {diag}[ρ0(t), 0,0, 0].
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