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

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 ρ=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. (Phys. Rev. Lett. 4: 375, 1960) that the gravitational mass of a neutral point particle is zero: m=0. And since, a dust is a mere collection of neutral point particles, unlike a continuous hydrodynamic fluid, its density ρ=mn=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 et al., Phys. Part. Nucl. 37: 317, 2006; Kiselev et al., Theor. Math. Phys. 164: 972, 2010; Mitra, J. Math. Phys. 50: 042502, 2009a; Suggett, J. Phys. A 12: 375 1979b). Interestingly, this result is in agreement with the intuition of Oppenheimer and Snyder (Phys. Rev. 56: 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.”