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

TL;DR

This paper challenges the traditional view of black hole formation by showing matter can cross the event horizon in finite time, denies the existence of gravitational singularities, and reinterprets Birkhoff's theorem in astrophysical contexts.

Contribution

It demonstrates that black holes form in finite time, matter never reaches the singularity, and the metric depends on the global matter distribution, revising classical understandings.

Findings

Matter crosses the event horizon in finite time.

Gravitational singularity does not exist in the physical universe.

The metric depends on the global matter distribution, not just local matter.

Abstract

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.