We provide analytical closed form solutions for the parallel transport along a bound geodesic in Kerr spacetime. This can be considered the lowest order approximation for the motion a spinning black hole in an extreme mass-ratio inspiral. As an illustration of the usefulness of our new found expressions we scope out the locations of spin-spin resonances in quasi-circular EMRIs. All solutions are given as functions of Mino time, which facilitates the decoupling of the equations of motion. To help physical interpretation, we also provide an analytical expression for the proper time along a geodesic as a function of Mino time.

中文翻译：

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克尔时空沿通用边界测地线平行输运的解析解

我们为沿克尔时空边界测地线的平行传输提供了解析封闭形式的解决方案。这可以被认为是极端质量比螺旋中旋转黑洞运动的最低阶近似值。为了说明我们新发现的表达式的有用性，我们确定了准圆形 EMRI 中自旋-自旋共振的位置。所有解都作为 Mino 时间的函数给出，这有助于运动方程的解耦。为了帮助物理解释，我们还提供了沿测地线的适当时间的解析表达式，作为米诺时间的函数。