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 l obeys the Hubble law v=Hl, and therefore galaxies at sufficiently great distance l 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.
American Journal of Physics
- Pub Date:
- January 2009
- General relativity and gravitation;
- REVTeX 4, 20 pages, accepted for publication in Am. J. Phys. Comments: edited version that will appear in the Am. J. Phys