  Inspired by some recent works of Tippett-Tsang and Mallary-Khanna-Price, we
present a new spacetime model containing closed timelike curves (CTCs). This
model is obtained postulating an ad hoc Lorentzian metric on $\mathbb{R}^4$,
which differs from the Minkowski metric only inside a spacetime region bounded
by two concentric tori. The resulting spacetime is topologically trivial, free
of curvature singularities and is both time and space orientable; besides, the
inner region enclosed by the smaller torus is flat and displays geodesic CTCs.
Our model shares some similarities with the time machine of Ori and Soen but it
has the advantage of a higher symmetry in the metric, allowing for the explicit
computation of a class of geodesics. The most remarkable feature emerging from
this computation is the presence of future-oriented timelike geodesics starting
from a point in the outer Minkowskian region, moving to the inner spacetime
region with CTCs, and then returning to the initial spatial position at an
earlier time; this means that time travel to the past can be performed by free
fall across our time machine. The amount of time travelled into the past is
determined quantitatively; this amount can be made arbitrarily large keeping
non-large the proper duration of the travel. An important drawback of the model
is the violation of the classical energy conditions, a common feature of many
time machines. Other problems emerge from our computations of the required
(negative) energy densities and of the tidal accelerations; these are small
only if the time machine is gigantic.
