The fallacy of Oppenheimer Snyder Collapse: no general relativistic Collapse at all, no black hole, no physical singularity

TL;DR

This paper argues that under general relativity, homogeneous dust collapse does not produce black holes or singularities, as the dust's density effectively becomes zero due to the nature of neutral point particles, challenging traditional collapse models.

Contribution

It demonstrates that homogeneous dust collapse in general relativity results in zero density, refuting the formation of black holes and singularities in such scenarios, based on Birkhoff's theorem and particle physics insights.

Findings

Density of dust is zero during collapse due to neutral point particles.

Homogeneous dust can collapse and expand without forming a black hole.

No physical singularity forms in homogeneous dust collapse according to this analysis.

Abstract

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."