标题： 奥本海默-斯奈德塌缩的谬误：根本没有广义相对论塌缩，没有黑洞，也没有物理奇点 显示英文标题

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

摘要： 通过将比克霍夫定理应用于均匀密度尘埃的一般相对论塌缩问题，我们直接证明了即使假设尘埃的真实数密度$n$是有限的，尘埃的密度$\rho=0$依然如此！ 这一精确结果背后的物理原因可以追溯到 Arnowitt 等人的观察： 中性点粒子的引力质量为零：$m=0$（PRL, 4, 375, 1960）。 由于尘埃只是{\em 中性点粒子，不像连续的流体}的集合，其密度为$\rho = m n=0$。 然而，发现对于$k=-1$，均匀尘埃可以在米尔恩宇宙的方式下特殊相对论地塌缩和膨胀。 因此，实际上，一般相对论均匀尘埃塌缩并不导致形成任何黑洞，这与许多先前的研究一致（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）。 有趣的是，这一结果也符合奥本海默和斯奈德的直觉（Phys. Rev. 56, p.456, 1939）： “物理上，这种奇点意味着用于能量-动量张量的表达式没有考虑到一些真正使奇点平滑的重要的物理事实。 此外，在发展的早期阶段，恒星不会有奇异的密度或压力，奇点不可能在有限的时间内发展。” 显示英文摘要

摘要： 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."