  By applying Birkhoff's theorem to the problem of the general relativistic
collapse of a uniform density dust, we directly show that the density of the
dust $\rho=0$ even when its proper number density $n$ would be assumed to be
finite! The physical reason behind this exact result can be traced back to the
observation of Arnowitt et al. that the gravitational mass of a neutral point
particle is zero: $m=0$ (PRL, 4, 375, 1960). And since, a dust is a mere
collection of {\em neutral point particles, unlike a continuous hydrodynamic
fluid}, its density $\rho = m n=0$. It is nonetheless found that for $k=-1$, a
homogeneous dust can collapse and expand special relativistically in the
fashion of a Milne universe. Thus, in reality, general relativistic homogeneous
dust collapse does not lead to the formation of any black hole in conformity of
many previous studies (Logunov, Mestverishvili, Kiselev, Phys.Part.Nucl. 37,
317, 2006; Kisevev, Logunov & Mestvirishvili, Theor. Math. Phys., 164, 972,
2010; Mitra, J. Math. Phys. 50, 042502, 2009; Suggett, J. Phys. A, 12, 375
1979).
  Interestingly, this result is in agreement with the intuition of Oppenheimer
& Snyder (Phys. Rev. 56, p.456, 1939) too:
  "Physically such a singularity would mean that the expressions used for the
energy-momentum tensor does not take into account some essential physical fact
which would really smooth the singularity out. Further, a star in its early
stages of development would not possess a singular density or pressure, it is
impossible for a singularity to develop in a finite time."
