由稳态差速旋转无旋柱形流体源产生的内部时空：各向异性压力
Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids: anisotropic pressure
AI总结：
本文将刚性旋转无旋柱形流体的各向异性压力内部时空推广到差速旋转，给出轴向与方位角压力解的构造方法及物理良好示例，并发现径向压力情形的四类解中一类可完全积分且物理良好。
摘要：
在最近的一系列论文中，展示了由稳态刚性旋转流体柱产生的新的精确解析内部时空。首先考虑了具有轴向压力的流体，然后是理想流体，接着是具有方位角方向压力的流体，最后是压力沿径向取向的流体。理想流体构型随后被推广到差速旋转情形。在本文中，对于差速旋转流体，依次考虑了类似于刚性旋转运动研究所涉及的三种不同各向异性压力情形。针对轴向压力和方位角压力情形，展示了生成场方程数学解的一般方法以及物理性质良好的示例。关于径向压力流体，相应的 Einstein 方程自然产生四类解，其中一类在被完全积分后表现出物理性质良好的解。
英文摘要：
In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid, followed by a fluid with an azimuthally directed pressure, and, finally, by a fluid where the pressure is radially oriented. The perfect fluid configuration has subsequently been extended to the case of differential rotation. In the present paper, three different cases of anisotropic pressure analogous to those studied for rigidly rotating motion are considered in turn for differentially rotating fluids. General methods for generating mathematical solutions to the field equations and physically well-behaved examples are displayed for the axial and azimuthal pressure cases. As regards radial pressure fluids, four classes of solutions naturally emerge from the corresponding Einstein's equations, among which one class, after being fully integrated, exhibits physically well-behaved solutions.
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