A stationary and axisymmetric (in fact circular) metric is reviewed which describes the first-order perturbation of a Schwarzschild black-hole space-time due to a rotating finite thin disc encircling the hole symmetrically. The key Green functions of the problem (corresponding to an infinitesimally thin ring)—the one for the gravitational potential and the one for the dragging angular velocity—were already derived, in terms of infinite series, by Will in 1974, but we have now put them into closed forms using elliptic integrals. Such forms are more practical for numerical evaluation and for integration in problems involving extended sources. This last point mostly remains difficult, but we illustrate that it may be workable by using the simple case of a finite thin disc with constant Newtonian surface density.

中文翻译：

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围绕Schwarzschild黑洞旋转光盘

回顾了静态和轴对称（实际上是圆形）的度量，该度量描述了由于旋转有限的薄盘对称地环绕孔而导致的Schwarzschild黑洞时空的一阶扰动。问题的关键格林函数（对应于一个无限薄的环）-一个用于重力势和一个用于拖动角速度-已由威尔在1974年以无限级数推导，但是现在使用椭圆积分将它们变成封闭形式。这样的形式对于数值评估和在涉及扩展来源的问题中的整合更为实用。最后一点仍然很困难，但是我们说明，通过使用具有恒定牛顿表面密度的有限薄盘的简单情况，它可能是可行的。