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

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

2006-05-06

arxiv.org/abs/gr-qc/0605037v1

Int.J.Mod.Phys. D15 (2006) 1183-1198

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, 2 EPS figures; to appear in the International Journal of Modern Physics D

Scientific paper

10.1142/S0218271806008899

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.

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