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首页> 外文期刊>Gravitation and Cosmology: G&C >Revisiting the Old Problem of General-Relativistic Adiabatic Collapse of a Uniform-Density Self-Gravitating Sphere
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Revisiting the Old Problem of General-Relativistic Adiabatic Collapse of a Uniform-Density Self-Gravitating Sphere

机译：重新审视均匀密度自重球的广义相对论绝热塌陷的老问题

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摘要

The problem of general-relativistic adiabatic collapse of a uniform-density perfect sphere has been studied since Wyman (Phys. Rev. 70, 396, (1946)) [1]. Apparently, there could be bouncing and oscillating solutions in such a case, as claimed by numerous authors since then. Consequently, various authors invoked such models for explaining pulsations of compact objects. However, here, for this age-old problem, we prove that for an assumed nonstatic adiabatically evolving sphere, density homogeneity implies (isotropic) pressure homogeneity too. This proof is based on the simple fact that in general relativity (GR), given one time coordinate t, one can employ another time coordinate t → t_* = f(t) without any loss of generality. Since this proof does not use any exterior boundary condition, it is valid in a cosmological scenario too. However, here we focus on the evolution of an isolated sphere having a boundary. And the proof obtained here shows that a uniform-density perfect fluid collapse can occur only if the (isotropic) pressure is p = 0, i.e., only when the problem is reduced to the one treated by Oppenheimer and Snyder. For such an isolated sphere, we offer a supporting proof. This result is important and nontrivial because in the past 65 years innumerable authors working on this problem failed to see that the collapse of a supposed homogeneous sphere is (actually) synonymous to the old Oppenheimer–Snyder problem.
机译：自Wyman以来，一直研究均匀密度完美球体的广义相对论绝热塌陷问题（Phys。Rev. 70，396，（1946））[1]。显然，在这种情况下，可能会有跳动和振荡的解决方案，此后许多作者都宣称。因此，各种作者引用了这种模型来解释紧凑物体的脉动。但是，在这里，对于这个古老的问题，我们证明对于假定的非静态绝热演化球体，密度均匀性也意味着（各向同性）压力均匀性。该证明基于以下简单事实：在广义相对论（GR）中，给定一个时间坐标t，可以使用另一时间坐标t→t_ * = f（t），而不会失去任何一般性。由于该证明不使用任何外部边界条件，因此在宇宙学场景中也是有效的。但是，在这里，我们着重讨论具有边界的孤立球体的演化。并且在此获得的证明表明，仅当（各向同性）压力为p = 0时，即仅当问题减少到由Oppenheimer和Snyder处理的问题时，才可能发生均匀密度的理想流体坍塌。对于这样一个孤立的领域，我们提供了证明。这个结果很重要而且很重要，因为在过去的65年中，无数的研究该问题的作者未能看到一个所谓的均匀球体的坍塌实际上是旧的Oppenheimer-Snyder问题的同义词。

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