是否有具有均匀能量密度的模型？
Are there any models with homogeneous energy density?
摘要：
通过应用最近的方法-基于广义相对论中的四分体形式主义和黎曼张量的正交分裂-简单的球形静态情况下，我们发现，唯一的静态解均匀能量密度是史瓦西解，并没有球对称的动态解与均匀能量密度假设一致。最后，一个循环的等价性之间的最常见的条件考虑在球对称的情况下：均匀的密度，各向同性的压力，共形平坦度和无剪切条件。我们证明，由于在物质分布的中心的规则性条件，两个条件的实施必然导致静态的情况下。
英文摘要：
By applying a recent method --based on a tetrad formalism in General Relativity and the orthogonal splitting of the Riemann tensor-- to the simple spherical static case, we found that the only static solution with homogeneous energy density is the Schwarzschild solution and that there are no spherically symmetric dynamic solutions consistent with the homogeneous energy density assumption. Finally, a circular equivalence is shown among the most frequent conditions considered in the spherical symmetric case: homogeneous density, isotropy in pressures, conformally flatness and shear-free conditions. We demonstrate that, due to the regularity conditions at the center of the matter distribution, the imposition of two conditions necessarily leads to the static case.
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