Einstein-Cartan理论中均匀自旋流体的坍缩和色散
Collapse and dispersal of a homogeneous spin fluid in Einstein-Cartan theory
摘要：
在本工作中，我们重新讨论了球对称均匀尘埃流体的引力坍缩过程，这被称为Oppenheimer-Snyder（OS）模型[1]。我们表明，这样的情况下，不会结束在时空奇点时，考虑到崩溃云内的费米子粒子的自旋自由度。为此，我们把恒星物体的物质含量看作是均匀的Weyssenhoff流体，它是广义相对论（GR）中理想流体的推广，包含了物质的自旋。采用均匀和各向同性FLRW度规的内部时空设置，它表明，物质的自旋，在负压的背景下，对引力的拉动和减速的动力学演化的崩溃在其后期阶段。我们的结果预示着一幅引力坍缩的图像，其中坍缩过程在有限半径处停止，该半径的值取决于初始构型。因此，我们表明，在OS模型中发生的时空奇点被取代的非奇异反弹，超过崩溃云重新扩展到无穷大。根据模型参数，可以找到坍缩云边界的最小值或相应的质量含量的阈值，低于该阈值可以避免层位形成。我们的结果得到了全面的数值分析的支持。
英文摘要：
In the present work, we revisit the process of gravitational collapse of a spherically symmetric homogeneous dust fluid which is known as the Oppenheimer-Snyder (OS) model [1]. We show that such a scenario would not end in a spacetime singularity when the spin degrees of freedom of fermionic particles within the collapsing cloud are taken into account. To this purpose, we take the matter content of the stellar object as a homogeneous Weyssenhoff fluid which is a generalization of perfect fluid in general relativity (GR) to include the spin of matter. Employing the homogeneous and isotropic FLRW metric for the interior spacetime setup, it is shown that the spin of matter, in the context of a negative pressure, acts against the pull of gravity and decelerates the dynamical evolution of the collapse in its later stages. Our results bode a picture of gravitational collapse in which the collapse process halts at a finite radius whose value depends on the initial configuration. We thus show that the spacetime singularity that occurs in the OS model is replaced by a non-singular bounce beyond which the collapsing cloud re-expands to infinity. Depending on the model parameters, one can find a minimum value for the boundary of the collapsing cloud or correspondingly a threshold value for the mass content below which the horizon formation can be avoided. Our results are supported by a thorough numerical analysis.
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