Semiclassical instability of dynamical warp drives

Warp drives are very interesting configurations in general relativity: At least theoretically, they provide a way to travel at superluminal speeds, albeit at the cost of requiring exotic matter to exist as solutions of Einstein’s equations. However, even if one succeeded in providing the necessary exotic matter to build them, it would still be necessary to check whether they would survive to the switching on of quantum effects. Semiclassical corrections to warp-drive geometries have been analyzed only for eternal warp-drive bubbles traveling at fixed superluminal speeds. Here, we investigate the more realistic case in which a superluminal warp drive is created out of an initially flat spacetime. First of all we analyze the causal structure of eternal and dynamical warp-drive spacetimes. Then we pass to the analysis of the renormalized stress-energy tensor (RSET) of a quantum field in these geometries. While the behavior of the RSET in these geometries has close similarities to that in the geometries associated with gravitational collapse, it shows dramatic differences too. On one side, an observer located at the center of a superluminal warp-drive bubble would generically experience a thermal flux of Hawking particles. On the other side, such Hawking flux will be generically extremely high if the exotic matter supporting the warp drive has its origin in a quantum field satisfying some form of quantum inequalities. Most of all, we find that the RSET will exponentially grow in time close to, and on, the front wall of the superluminal bubble. Consequently, one is led to conclude that the warp-drive geometries are unstable against semiclassical backreaction.

Figure 1

Lines of constant $u$ (solid lines) and $w$ (dashed lines) for the Alcubierre warp drive, $a=c=1$, $\alpha =2$.

Figure 2

Penrose diagram of an eternal warp drive. Lines of constant $r$ (solid lines) and of constant $t$ (dashed lines). Future and past horizons at $r=r_1$, $r_2$ (heavy dashed lines). The geometry can be extended to the future of ${\mathscr{H}}_C^{+}$ and ${\mathscr{H}}_R^{+}$ and to the past of ${\mathscr{H}}_C^{-}$ and ${\mathscr{H}}_L^{-}$.

Figure 3

Penrose diagram of a dynamic warp drive. Lines of constant $r$ (solid lines) and of constant $t$ (dashed lines). The lines of constant $r$ become null at the apparent horizons (heavy dashed lines).

Figure 4

Light rays propagating rightward (solid lines) and leftward (dashed lines) in the plane ($t$, $r$) in a warp-drive spacetime with velocity profile of Eq. (a2). The out region in which the geometry is a stationary warp drive is at $r<\pm \mathrm{arccosh}(t+1)$ (heavy solid lines). At $t<0$ the metric is Minkowskian. The horizons at $r_1$ and $r_2$ (heavy dashed lines) are formed at $T_H=1$. Please refer to Appendix  for details.