  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.
