  We set up a vacuum theory of gravity with an extra dimension of vanishing
proper length. The most general solution to the field equations are presented.
This formulation is free of Kaluza-Klein modes and does not allow the
propagation of gravitons along the invisible fifth direction. Apart from a
vacuum energy and radiation, the associated emergent theory exhibits a
nonpropagating vector-tensor multiplet which has no analogue in standard
Einstein gravity. It is naturally inert, obeys a bounded equation of state and
has coupling properties radically different from ordinary matter. Based on
these distinctive features, we propose that this geometric multiplet could
supercede the hypothetical ``dark matter''. As further evidence in support of
this possibility, we show that the galactic rotation curves are predicted to be
asymptotically flat.
