On the Solution to the "Frozen Star" Paradox, Nature of Astrophysical
  Black Holes, non-Existence of Gravitational Singularity in the Physical
  Universe and Applicability of the Birkhoff's Theorem
  Oppenheimer and Snyder found in 1939 that gravitational collapse in vacuum
produces a "frozen star", i.e., the collapsing matter only asymptotically
approaches the gravitational radius (event horizon) of the mass, but never
crosses it within a finite time for an external observer. Based upon our recent
publication on the problem of gravitational collapse in the physical universe
for an external observer, the following results are reported here: (1) Matter
can indeed fall across the event horizon within a finite time and thus BHs,
rather than "frozen stars", are formed in gravitational collapse in the
physical universe. (2) Matter fallen into an astrophysical black hole can never
arrive at the exact center; the exact interior distribution of matter depends
upon the history of the collapse process. Therefore gravitational singularity
does not exist in the physical universe. (3) The metric at any radius is
determined by the global distribution of matter, i.e., not only by the matter
inside the given radius, even in a spherically symmetric and pressureless
gravitational system. This is qualitatively different from the Newtonian
gravity and the common (mis)understanding of the Birkhoff's Theorem. This
result does not contract the "Lemaitre-Tolman-Bondi" solution for an external
observer.
