标题： 各向异性圆柱流体的定态刚性旋转研究及广义相对论的新精确内部解。 4. 径向压强 显示英文标题

标题： Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. 4. Radial pressure

摘要： 本文属于一个系列文章，其中使用为该目的构建的新精确解来研究各向异性压力对刚性旋转流体引力性质的影响。 为了数学简化，考虑了平稳性和圆柱对称性，这暗示存在三个Killing矢量。 此外，依次让两个压力分量为零。 在论文1和2中，压力是轴向的，而在论文3中，压力是方位的。 在本论文4中，考虑了径向压力。 由于从场方程中出现了一个分为三部分的通用微分方程，可以考虑三种不同类别的解。 其中两种只能部分积分。 另一种则完全积分，产生了一组具有负压力的解。 遇到负压力的物理过程被描绘出来，并为此类解提供了相当坚实的基础。 此外，这些完全积分的解满足轴对称条件，但它们不满足所谓的“正则性条件”。 但是，由于它们的Kretschmann标量在轴上不会发散，这一特性必须被认为是报告了一个单纯的坐标奇点。 最后，这些解与适当的外部真空匹配，对定义该类每个解的两个常数参数施加了其他约束。 这里显示的结果应结合该系列中其他四篇论文所描绘的内容进行解释。 显示英文摘要

摘要： This article belongs to a series where the influence of anisotropic pressure on the gravitational properties of rigidly rotating fluids is studied using new exactsolutions of GR constructed for the purpose. For mathematical simplification, stationarity and cylindrical symmetry implying three Killing vectors are considered. Moreover, two pressure components are set to vanish in turn. In Papers 1 and 2 the pressure is axially directed, while it is azimuthal in Paper 3. In present Paper 4, a radially directed pressure is considered. Since a generic differential equation, split into three parts, emerges from the field equations, three different classes of solutions can be considered. Two could only be partially integrated. The other one, that is fully integrated, yields a set of solutions with negative pressure. Physical processes where a negative pressure is encountered are depicted and give a rather solid foundation to this class of solutions. Moreover, these fully integrated solutions satisfy the axisymmetry condition while they do not verify the so-called "regularity condition". But, since their Kretschmann scalar does not diverge on the axis, this feature must be considered as reporting a mere coordinate singularity. Finally, the matching of these solutions to an exterior appropriate vacuum enforce other constraints on the two constant parameters defining each solution in the class. The results displayed here deserve to be interpreted in the light of those depicted in the other four papers in the series.