Warp Drives and Closed Timelike Curves

TL;DR

This paper constructs a mathematical model using generalized warp drives in curved spacetime to demonstrate how faster-than-light travel can theoretically enable time travel via closed timelike curves, highlighting energy condition violations.

Contribution

It introduces a novel warp drive metric with a non-unit lapse function and demonstrates how two such drives can be combined to form a closed timelike geodesic in general relativity.

Findings

A generalized warp drive metric allows frame switching in curved spacetime.

Two warp drives can be glued to create a closed timelike curve.

The model shows violations of the weak energy condition.

Abstract

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.