Adiabatic theory in Kerr spacetimes

Abstract

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.