  Wherever one talks of dark matter, one does so where there is an observable
matter and an associated unsolved dynamical issue to be settled. We promote
this observation to the status of an axiom and conjecture that there is a dark
companion to every baryonic matter, subject to certain rules as regards its
size, distribution. To pursue the proposition in a systematic way we resort to
the rotation curves of spiral galaxies. They have non classical features.
First, we design a spacetime metric around the galaxy to accommodate these
features. Next we calculate the density and pressure of a hypothetical dark
matter that could generate such a spacetime. In the weak field regime and for a
spherical distribution of mass $M$, we are able to assign a dark perfect gas
companion, whose density is almost proportional to $M^{1/2}$ and fades away
almost as $r^{-2}$. However, in view of this orderly relation between the
observable mass and its dark companion, one may choose to interpret the whole
scenario as an alternative theory of gravitation.
