Impossibility of superluminal travel in Lorentz violating theories

TL;DR

This paper investigates the stability of warp drives under Lorentz violation at high energies, finding that they remain unstable due to quantum effects, thus supporting the protection of causality.

Contribution

It demonstrates that warp drives are unstable even with Lorentz violation and dispersion, revealing different instability mechanisms for subluminal and superluminal cases.

Findings

Warp drives are quantum mechanically unstable even with Lorentz violation.

Subluminal dispersion causes exponential flux amplification via black-hole laser effects.

Superluminal dispersion leads to linear growth of flux due to infrared effects.

Abstract

Warp drives are space-times allowing for superluminal travel. However, they are quantum mechanically unstable because they produce a Hawking-like radiation which is blue shifted at their front wall without any bound. We reexamine this instability when local Lorentz invariance is violated at ultrahigh energy by dispersion, as in some theories of quantum gravity. Interestingly, even though the ultraviolet divergence is now regulated, warp drives are still unstable. Moreover the type of instability is different whether one uses a subluminal or a superluminal dispersion relation. In the first case, a black-hole laser yields an exponential amplification of the emitted flux whereas, in the second, infrared effects produce a linear growth of that flux. These results suggest that chronology could still be protected when violating Lorentz invariance.