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.

在最近的一系列论文中，展示了由静止的刚性旋转流体圆柱体来源的新的精确分析内部时空。首先考虑具有轴向定向压力的流体，然后考虑完美流体，接着考虑具有方位定向压力的流体，最后考虑压力径向定向的流体。完美的流体配置随后被扩展到差动旋转的情况。在本文中，对于差动旋转流体，依次考虑与刚性旋转运动研究类似的各向异性压力的三种不同情况。针对轴向和方位角压力情况，显示了生成场方程数学解的一般方法以及物理上表现良好的示例。对于径向压力流体，相应的爱因斯坦方程自然会出现四类解，其中一类在完全积分后表现出物理上良好的解。