On the warp drive space-time

TL;DR

This paper investigates the quantum stability of a two-dimensional warp drive spacetime, showing it can be stable without divergent quantum effects and connecting it to gravitational kinks, thus advancing warp drive theoretical models.

Contribution

It demonstrates the quantum stability of the warp drive spacetime and links it to gravitational kinks, extending the Alcubierre metric to a nonstatic, multi-patch metric.

Findings

Quantum fluctuations do not cause divergences at the horizon.

The warp drive satisfies Ford's negative energy-time inequality.

A connection between warp drives and gravitational kinks is established.

Abstract

In this paper the problem of the quantum stability of the two-dimensional warp drive spacetime moving with an apparent faster than light velocity is considered. We regard as a maximum extension beyond the event horizon of that spacetime its embedding in a three-dimensional Minkowskian space with the topology of the corresponding Misner space. It is obtained that the interior of the spaceship bubble becomes then a multiply connected nonchronal region with closed timelike curves and that the most natural vacuum allows quantum fluctuations which do not induce any divergent behaviour of the re-normalized stress-energy tensor, even on the event (Cauchy) chronology horizon. In such a case, the horizon encloses closed timelike curves only at scales close to the Planck length, so that the warp drive satisfies the Ford's negative energy-time inequality. Also found is a connection between the superluminal two-dimensional warp drive space and two-dimensional gravitational kinks. This connection allows us to generalize the considered Alcubierre metric to a standard, nonstatic metric which is only describable on two different coordinate patches