The Orbital and Epicyclic Frequencies in Axially Symmetric and Stationary Spacetime

Abstract

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.