Astronomy and Astrophysics – Astrophysics
Scientific paper
2008-03-18
Am.J.Phys.77:59-66,2009
Astronomy and Astrophysics
Astrophysics
REVTeX 4, 20 pages, accepted for publication in Am. J. Phys. Comments: edited version that will appear in the Am. J. Phys
Scientific paper
10.1119/1.2987790
The cosmological Robertson-Walker metric of general relativity is often said to have the consequences that (1) the recessional velocity $v$ of a galaxy at proper distance $\ell$ obeys the Hubble law $v=H\ell$, and therefore galaxies at sufficiently great distance $\ell$ are receding faster than the speed of light $c$; (2) faster than light recession does not violate special relativity theory because the latter is not applicable to the cosmological problem, and because ``space itself is receding'' faster than $c$ at great distance, and it is velocity relative to local space that is limited by $c$, not the velocity of distant objects relative to nearby ones; (3) we can see galaxies receding faster than the speed of light; and (4) the cosmological redshift is not a Doppler shift, but is due to a stretching of photon wavelength during propagation in an expanding universe. We present a particular Robertson-Walker metric (an empty universe metric) for which a coordinate transformation shows that none of these interpretation necessarily holds. The resulting paradoxes of interpretation lead to a deeper understanding of the meaning of the cosmological metric.
Burns Maurice S.
Cook Richard J.
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