Magnification of classical multimessenger signals in stationary and axisymmetric spacetimes with separable equations of motion

When photons, gravitational waves, and massive particles such as neutrinos are gravitationally lensed the signals detected by telescopes or detectors on and around Earth are usually either magnified or demagnified. However, for stationary and axisymmetric spacetimes conventional methods for calculating the magnification factor usually only allow one to calculate it relative to the spacetime position of the source but not with respect to the source's reference frame. While this may be sufficient when we want to investigate the properties of the lens, when we want to investigate the source and its properties we need to relate the detected signals to the same signals in the reference frame of their source. In this paper we will now show that for stationary and axisymmetric spacetimes which possess a Carter constant, we can use the constants of motion and the tetrad formalism to derive a magnification factor which relates a signal detected in the reference frame of an observer to the same signal in the reference frame of its source.