均匀密度剪切流体
On Shearing Fluids with Homogeneous Densities
摘要：
本文研究了同动坐标系下剪切球对称均匀密度流体的性质。结果表明，理想流体的四速度展开是均匀的，而其剪切是由时间M（t）的任意函数产生的，与分布的质量函数有关。该函数与密度存在函数关系。场方程简化为两个耦合的一阶常微分方程的度量系数，g 11和g 22。假设M是密度的线性函数，我们已经探索了一类解。这一类包含了完整的无剪力解类。我们已经讨论了Kustaanheimo（1947）的工作，并注意到它涉及具有各向异性压力的无剪切流体。它示出的流体的各向异性的特征在于由一个任意函数的时间。我们已经讨论了与无剪切解决方案相关的历史优先事项和证书的一些问题。Mitra最近提出的有争议的主张（2011年，2012年）也得到了处理。我们发现奇异性与流体的剪切运动密切相关。因此，有必要重新审视先前在共动坐标系中获得的解。关键词（以“-”分隔）剪切溶液-理想流体-均匀密度
英文摘要：
In this paper, we study shearing spherically symmetric homogeneous density fluids in comoving coordinates. It is found that the expansion of the four-velocity of a perfect fluid is homogeneous, whereas its shear is generated by an arbitrary function of time M(t), related to the mass function of the distribution. This function is found to bear a functional relationship with density. The field equations are reduced to two coupled first order ordinary differential equations for the metric coefficients, g 11 and g 22. We have explored a class of solutions assuming that M is a linear function of the density. This class embodies, as a subcase, the complete class of shear-free solutions. We have discussed the off quoted work of Kustaanheimo (1947) and have noted that it deals with shear-free fluids having anisotropic pressure. It is shown that the anisotropy of the fluid is characterized by an arbitrary function of time. We have discussed some issues of historical priorities and credentials related to shear-free solutions. Recent controversial claims by Mitra (2011, 2012) have also been addressed. We found that the singularity and the shearing motion of the fluid are closely related. Hence, there is a need for fresh look to the solutions obtained earlier in comoving coordinates. Keywords (separated by '-') Shearing solution - Perfect fluids - Homogeneous density
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