We outline the essential features of the adiabatic theory and demonstrate how test particle motion in general relativity may be investigated using it. The theory relies on adiabatic invariants and vector elements of the orbits. We derive a specific representation of the Kerr metric in harmonic coordinates, which enables us to obtain a general formula for the perihelion shift of test particles orbiting on the non-equatorial plane of a rotating central object. This proves the applicability of the adiabatic theory in Einstein’s gravity. We demonstrate that, for the individual effects of the gravitational source mass and angular momentum up to the second order, the principle of superposition is satisfied. We show that, in addition to its simplicity, the adiabatic theory produces correct results that, in the limiting cases, correspond to the ones reported in the literature.

我们概述了绝热理论的基本特征，并演示了如何使用它来研究广义相对论中的测试粒子运动。该理论依赖于绝热不变量和轨道矢量元素。我们推导了克尔度量在调和坐标中的具体表示，这使我们能够获得在旋转中心物体的非赤道平面上轨道运行的测试粒子的近日点位移的通用公式。这证明了绝热理论在爱因斯坦引力中的适用性。我们证明，对于高达二阶的引力源质量和角动量的个体效应，满足叠加原理。我们表明，除了简单性之外，绝热理论还产生了正确的结果，在极限情况下，与文献中报告的结果相对应。