Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-01-27
J.Geom.Phys. 56 (2006) 813-829
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages, 5 figures. Since "lightlike distance" is in fact the known "affine distance", the notation has been changed
Scientific paper
10.1016/j.geomphys.2005.05.001
We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light aberration. We obtain that comoving observers observe the same light ray with the same frequency and direction, and so gravitational redshift effect is a particular case of Doppler effect. We also define a distance between an observer and the events that it observes, that coincides with the known affine distance. We show that affine distance is a particular case of radar distance in the Minkowski space-time and generalizes the proper radial distance in the Schwarzschild space-time. Finally, we show that affine distance gives us a new concept of distance in Robertson-Walker space-times, according to Hubble law.
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