Doppler Effects from Bending of Light Rays in Curved Space-Times

TL;DR

This paper investigates how light bending in curved space-time affects Doppler frequency shifts, especially considering the gravitational influence of rotating and quadrupole-moment sources, with potential applications in planetary measurements.

Contribution

It provides a detailed analysis of Doppler effects caused by light bending in weak gravitational fields, including contributions from quadrupole moments and rotation, using the PPN formalism.

Findings

Numerical estimates for Doppler shifts in planetary gravitational fields.

Potential to measure planetary quadrupole moments via Doppler effect analysis.

Preliminary evidence that light bending influences frequency shifts in measurable ways.

Abstract

We study Doppler effects in curved space-time, i.e. the frequency shifts induced on electromagnetic signals propagating in the gravitational field. In particular, we focus on the frequency shift due to the bending of light rays in weak gravitational fields. We consider, using the PPN formalism, the gravitational field of an axially symmetric distribution of mass. The zeroth order, i.e. the sphere, is studied then passing to the contribution of the quadrupole moment, and finally to the case of a rotating source. We give numerical estimates for situations of physical interest, and by a very preliminary analysis, we argue that analyzing the Doppler effect could lead, in principle, in the foreseeable future, to the measurement of the quadrupole moment of the giant planets of the Solar System.