相对论旋转球体和圆柱体引起的离心力
Centrifugal force induced by relativistically rotating spheroids and cylinders
摘要：
本文从牛顿球壳的引力势出发，讨论麦克斯韦理论中带电旋转长球壳。特别地，我们考虑两个共焦的带电荷的壳层，它们以这样一种方式反向旋转，即外壳层外没有磁场。在爱因斯坦理论中，我们在长椭球几乎是圆柱形的区域求解恩斯特方程;在赤道区域，精确的刘易斯“旋转圆柱”解是由空间束缚系统的极限过程导出的。在第二部分中，我们分析了两个圆柱壳在相反的方向旋转，在这样一种方式，静态Levi-Civita度规产生的外部和没有角动量通量逃逸到无穷大。因此，在这个模型中，没有任何近似或解释上的困难，表现出内圆柱内部平坦空间中的局部惯性系的旋转。内圆筒内相对于从无穷远看不旋转的轴保持静止的测试颗粒经历离心力。虽然那里的时空是闵可夫斯基的，但是这个空间是旋转的，所以相对于局部惯性系，粒子是在绕着一个圆形轨道运动。
英文摘要：
Starting from the gravitational potential of a Newtonian spheroidal shell we discuss electrically charged rotating prolate spheroidal shells in the Maxwell theory. In particular we consider two confocal charged shells which rotate oppositely in such a way that there is no magnetic field outside the outer shell. In the Einstein theory we solve the Ernst equations in the region where the long prolate spheroids are almost cylindrical; in equatorial regions the exact Lewis "rotating cylindrical" solution is so derived by a limiting procedure from a spatially bound system. In the second part we analyze two cylindrical shells rotating in opposite directions in such a way that the static Levi-Civita metric is produced outside and no angular momentum flux escapes to infinity. The rotation of the local inertial frames in flat space inside the inner cylinder is thus exhibited without any approximation or interpretational difficulties within this model. A test particle within the inner cylinder kept at rest with respect to axes that do not rotate as seen from infinity experiences a centrifugal force. Although the spacetime there is Minkowskian out to the inner cylinder nevertheless that space has been induced to rotate, so relative to the local inertial frame the particle is traversing a circular orbit.
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