  It is commonly accepted that superluminal travel may be used to facilitate
time travel. This is a purely special-relativistic argument, using the fact
that for observers in two frames of reference, separated by a spacelike
interval, the non-causal (spacelike) future of one observer includes part of
the causal past of the other. In this paper we provide a concrete realization
of this argument in a curved general-relativistic spacetime, using warp drives
as the means of faster-than-light travel. By generalizing the usual warp drive
metric to allow for a non-unit lapse function, we allow the warp drive to
switch between reference frames in a purely geometric way. With an additional
modification allowing the warp drive to have compact support, this permits us
to glue two warp drives together to construct a closed timelike geodesic, such
that a test particle following the geodesics of the two warp drives travels
back to its own past. This provides a precise mathematical model for the
connection between faster-than-light travel and time travel in general
relativity, and the first such model to be explicitly formulated using two warp
drives. We also give a detailed discussion of weak energy condition violations
in the non-unit-lapse warp drive.
