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.

中文翻译：

---

曲速驱动和闭合类时曲线


人们普遍认为超光速旅行可以用来促进时间旅行。这是一个纯粹的狭义相对论论点，利用这样一个事实：对于两个参考系中的观察者来说，被一个类空间间隔分开，一个观察者的非因果（类空间）未来包括另一个观察者的因果过去的一部分。在本文中，我们使用曲速驱动器作为超光速旅行的手段，在弯曲的广义相对论时空中具体实现了这一论点。通过概括通常的扭曲驱动度量以允许非单位失效函数，我们允许扭曲驱动以纯几何方式在参考系之间切换。通过额外的修改，使曲速驱动器具有紧凑的支撑，这使我们能够将两个曲速驱动器粘​​合在一起以构建封闭的类时测地线，以便沿着两个曲速驱动器的测地线运行的测试粒子回到其自己的过去。这为广义相对论中超光速旅行和时间旅行之间的联系提供了一个精确的数学模型，也是第一个使用两个曲速驱动器明确制定的此类模型。我们还详细讨论了非单位跃迁曲速驱动中的弱能量条件违规。