When can information escape from a black hole through a warp bubble-like spacetime?

Question

It is well known that nothing can escape a black hole, including gravitational radiation. Many questions have been asked here about this topic, such as:

• Can gravitational waves escape a black hole?
• Can we detect gravitational waves generated from inside the event horizon of a black hole?
• Can gravitational waves escape from inside of black holes?
• How does gravity escape a black hole?

and they all have the same answer. Gravitational radiation cannot propagate faster than the speed of light.

On the other hand, it also seems to be generally agreed that if an Alcubierre drive is physically possible, one can theoretically use one to escape a black hole. (Could a ship equipped with Alcubierre drive theoretically escape from a black hole?)

Now an Alcubierre drive is essentially just a particular spacetime metric. You don't even need negative energy density to make one. In particular, it was recently shown that one can construct a superluminal soliton solution in general relativity using only positive energy densities.

Connecting these ideas, it seems that it should be possible, in principle, to fall through the event horizon of a black hole; construct an Alcubierre spacetime by manipulating a collection of very massive objects; and escape the event horizon with information from inside the black hole. Then my question is: where is the line between gravitational waves and Alcubierre spacetimes? Could there be other Alcubierre-like metrics that do not contain a full warp bubble, but still allow information to escape from a black hole?

Answer 1

There is a fundamental problem with this scheme: constructing a warp drive spacetime. The papers exploring such spacetimes all work by (1) assuming some negative energy density exotic matter to hold together the bubble, and (2) that the bubble already exists. (1) is problematic since we have never seen such exotic matter, but (2) is more fundamental: there are to my knowledge no warp drive spacetimes that start locally as flattish spacetime, become a spacetime with a bubble, and then stop having a bubble.

Indeed, there are theorems in general relativity that state that if you have a Cauchy surface (a "flat" initial state at some coordinate time) then you will always retain that topology at later times. However, these theorems are broken by the exotic matter assumption, so how much they can be trusted here is debatable. Similarly the topological censorship theorem fails here. The issue here is that by allowing arbitrary exotic fields we can make spacetime manifolds with almost any crazy topology... but these fields are not guaranteed to exist or even be possible.

But if you can make warp drive spacetimes out of positive matter densities then the second difficulty gets you instead. Now those theorems apply, and you cannot get the nontrivial topology of spacetime trajectories you want from a warp drive. Even disregarding the issue of what the black hole would do to them.

Answer 2

Great question! Anyone who could answer that question would probably publish these results in some high-impact, prestigious, indexed journal.

In Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory, Lentz's idea is very creative and sophisticated, but it is still an idea and not a definite model for a warp drive. One has to define a metric with warp drive properties. Couple an energy-momentum tensor and solve Einstein equations, finding a KdV-type equation in terms of the shift vector governing the dynamics of the warp bubble, then defining the boundary and initial conditions from energy conditions, the null divergence of the energy-momentum tensor, and other properties imposing energy and matter density to be positive. This spacetime cannot allow closed timelike curves.

Jose Natario in Warp Drive With Zero Expansion demonstrated that warp drive with flat Cauchy surfaces will eventually violate Weak energy conditions because of no expansion volume, and a non-zero expansion will violate strong energy conditions. This is why in an Alcubierre drive, Eulerian observers will always perceive a warp bubble with non-positive energy density.

Also, in Warp Drive Basics, Alcubierre and Lobo demonstrated that there is an event horizon inside the warp bubble. So, the warp bubble may behave as a black (or white!) hole.

So, there is a very thin margin for constructing a physical warp drive with no pathologies. There are a lot of caveats.

Answer 3

The reality is that the question you are asking is just too hard to answer at the moment.

The state of the art can barely describe the properties of isolated warp drives solutions in flat space time, while this would be a warp drive falling in the curved geometry of a black hole. As the boundary conditions and assumptions of the most common warp solutions (e.g. Alcubierre) are invalidated, you would need to perform a numerical analysis to get accurate predictions.