On the Doppler effect for light from orbiting sources in Kerr-type metrics

TL;DR

This paper derives a comprehensive formula for the combined Doppler effect on light emitted by orbiting sources in Kerr-type metrics, connecting observational astronomy with relativistic physics.

Contribution

It introduces a unified formula for the gravitational and motional Doppler effects applicable to Kerr-type metrics, derived via multiple approaches.

Findings

The formula matches expected results in Kerr and Schwarzschild limits.

It applies to both stationary and moving sources in curved spacetime.

Connections between observational astronomy and relativity are clarified.

Abstract

A formula is derived for the combined motional and gravitational Doppler effect in general stationary axisymmetric metrics for a photon emitted parallel or antiparallel to the assumed circular orbital motion of its source. The same formula is derived from eikonal approximation and Killing vector approaches to elucidate connections between observational astronomy and modern Relativity. The formula yields expected results in the limits of a moving or stationary source in the exterior Kerr and Schwarzschild metrics and a moving source in flat space.