The matter in the Big-Bang model is dust and not any arbitrary perfect fluid

• Published in: Astrophysics and space science Vol. 333; no. 1; pp. 351 - 356
• Main Author: Mitra, Abhas
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-05-2011; Springer Nature B.V
• Subjects: Astrobiology; Astronomy; Astrophysics; Astrophysics and Astroparticles; Big Bang theory; Cosmology; Dust; Energy conservation; Fluid mechanics; Observations and Techniques; Original Article; Physics; Physics and Astronomy; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Cosmology; Friedmann-Robertson-Walker spacetime; Big-Bang model; General relativity; Gravitational collapse
• ISSN: 0004-640X; 1572-946X
• DOI: 10.1007/s10509-011-0635-8

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
),
. 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
because they intrinsically have the same energy momentum tensor
.