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Oppenheimer and Snyder found in 1939 that gravitational collapse in vacuumproduces a "frozen star", i.e., the collapsing matter only asymptoticallyapproaches the gravitational radius (event horizon) of the mass, but nevercrosses it within a finite time for an external observer. Based upon our recentpublication on the problem of gravitational collapse in the physical universefor an external observer, the following results are reported here: (1) Mattercan indeed fall across the event horizon within a finite time and thus BHs,rather than "frozen stars", are formed in gravitational collapse in thephysical universe. (2) Matter fallen into an astrophysical black hole can neverarrive at the exact center; the exact interior distribution of matter dependsupon the history of the collapse process. Therefore gravitational singularitydoes not exist in the physical universe. (3) The metric at any radius isdetermined by the global distribution of matter, i.e., not only by the matterinside the given radius, even in a spherically symmetric and pressurelessgravitational system. This is qualitatively different from the Newtoniangravity and the common (mis)understanding of the Birkhoff's Theorem. Thisresult does not contract the "Lemaitre-Tolman-Bondi" solution for an externalobserver.

international journal of modern physics d

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