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 (1003.1359v1)

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.

• The paper resolves the frozen star paradox by demonstrating that infalling matter crosses the event horizon in finite time.
• It reveals that astrophysical black holes do not harbor singularities, but exhibit matter distributions influenced by collapse history.
• The study shows that the local metric is affected by the global mass distribution, challenging the conventional use of Birkhoff’s theorem.

Overview of "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" by Shuang-Nan Zhang

The paper authored by Shuang-Nan Zhang addresses fundamental questions regarding gravitational collapse, particularly focusing on the "Frozen Star" paradox, the nature of black holes (BHs), the non-existence of singularities, and the applicability of Birkhoff's theorem in the physical universe. The results presented challenge some traditional interpretations of general relativity and black hole physics.

Core Results and Discussions

1. Resolution of the "Frozen Star" Paradox: The paper builds on the gravitational collapse model initially described by Oppenheimer and Snyder, which predicted that from the perspective of an external observer, infalling matter never actually crosses the event horizon, resulting in a "frozen star." Zhang refutes this by demonstrating that matter indeed crosses the event horizon in finite time, leading to the formation of black holes in the physical universe.
2. Non-Existence of Gravitational Singularity: The paper posits that matter falling into a black hole never reaches a singularity. It contends that astrophysical black holes are not singularities but rather entities where the exact distribution of matter depends on the collapse history. Consequently, singularities, which are often considered in theoretical models, are argued to be non-existent in the observable universe.
3. Global Metric Dependency and Birkhoff's Theorem: Challenging the conventional understanding of the Birkhoff's theorem, the paper reveals that the metric at a given radius is influenced by the entire global distribution of matter, not just the interior mass. This stands in contrast to Newtonian gravity and implies a complex interaction in a spherically symmetric and pressureless system. This has significant implications for interpreting phenomena like gravitational lensing and delays in signal propagation.

Implications of the Research

• Astrophysical Understanding: The conclusions drawn impact the established models of black hole formation and characteristics, suggesting that further observational and theoretical work is needed to reconcile these findings with existing astrophysical phenomena.
• General Relativity and Cosmology: By contending the non-existence of singularities, the work provokes a reconsideration of the fundamental solutions within general relativity, potentially affecting how black holes are modeled in cosmological simulations and theories.
• Future Observational Strategies: Given the claims about global metric dependency and signal delays, astronomers and astrophysicists may need to revise methods for estimating mass distributions in vast cosmic structures, potentially influencing dark matter research.

Speculations on Future Developments

Future studies could expand on the numerical simulations and mathematical models used in this research to further elucidate the behaviors of collapsing matter and the formation of black holes. More comprehensive observational data from gravitational wave detections and other high-precision astrophysical measurements may provide tests for these bold claims, either supporting or refuting the proposed non-existence of singularities and the described global influences on local metrics. As AI tools improve, they may assist in the complex simulations necessary to understand these intricate gravitational phenomena.