  We consider a theory of gravity with a hidden extra-dimension and
metric-dependent torsion. A set of physically motivated constraints are imposed
on the geometry so that the torsion stays confined to the extra-dimension and
the extra-dimension stays hidden at the level of four dimensional geodesic
motion. At the kinematic level, the theory maps on to General Relativity, but
the dynamical field equations that follow from the action principle deviate
markedly from the standard Einstein equations. We study static spherically
symmetric vacuum solutions and homogeneous-isotropic cosmological solutions
that emerge from the field equations. In both cases, we find solutions of
significant physical interest. Most notably, we find positive mass solutions
with naked singularity that match the well known Schwarzschild solution at
large distances but lack an event horizon. In the cosmological context, we find
oscillatory scenario in contrast to the inevitable, singular big bang of the
standard cosmology.
