Motivated by observational evidence of the electromagnetic signal from the X-ray binary system known as quasi-periodic oscillations in the light curves of astrophysical black holes or neutron stars, we examined the general relativity and alternative theory of gravity in the strong gravity regime. The orbital and epicyclic motion of test particles in general axially symmetric spacetime was investigated. We provide a general description to derive the exact analytical expressions for the fundamental frequencies, namely, Keplerian epicyclic (radial and vertical) frequencies of test particles in an arbitrary axisymmetric and stationary spacetime. The detailed derivation of the expressions for the orbital and epicyclic frequencies of test particles orbiting around the Kerr–Newman-NUT black hole is also shown.

中文翻译：

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轴对称和静止时空中的轨道和周转频率

受到来自 X 射线双星系统的电磁信号的观测证据的启发，该系统被称为天体物理黑洞或中子星光变曲线中的准周期振荡，我们研究了强引力区中的广义相对论和替代引力理论。研究了一般轴对称时空中测试粒子的轨道和周转运动。我们提供了一个一般描述来推导基本频率的精确解析表达式，即任意轴对称和静止时空中的测试粒子的开普勒行星（径向和垂直）频率。还显示了围绕 Kerr-Newman-NUT 黑洞运行的测试粒子的轨道和周转频率表达式的详细推导。