Are they trying to say that if there was something that could move faster than light then it can escape? If that's is forbidden by laws of nature, then how did they determined that this is possible?
Since you can't get out of a black hole normally, the only way to get out is by reversing time. I.e., going faster than light might be an option to get out of a black hole.
Of course, doing so is nonsense, but the maths work out.
The constant speed is actually the speed of a massless object through spacetime. It just so happens to be that photons have no mass. Also, going at high speed wouldn't make your life pass in slow motion to you. It would simply look that way to an observer who was moving vastly slower than you. The dilation in time is as a result of difference in relative velocities, rather than the speed of time changing.
This is also why the part about "go faster than the speed of light" doesn't make sense in physics. Motion is a four dimensional vector, with three points giving a point position, and the forth giving velocity through spacetime. Thus you wouldn't be travelling through "time" backwards, but through spacetime backwards.
Hope that helps. For more information, you may want to read up on the geometry of Minkowski spacetime.
The important thing in causality is the concept of the light cone. For things that happen far apart enough that the light cones don't interfere with each other, causality doesn't matter. One could happen first, or the other. It's only when you consider two things where the interaction occurs that the propagation matters.
Clearing this up a little further, having just read your other comment, the causal link between events and the speed by which information propagates is as a result of c, not the cause of it.
0: https://www.wikiwand.com/en/Light_cone 1: http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spa...
The "speed of light" is not really the speed of light - it's the speed of causality.
When one measures the "speed of light", one is measuring the time taken between two events;
Event 1 : the moment a beam of light was emitted from a location.
Event 2 : the moment that beam of light was detected at some other location.
The time taken for light to traverse between its initial emission and its subsequent detection, is basically the speed of causality.
For me that was a bit of an epiphany, and makes it much easier for me to understand the concept of spacetime that previously had me befuddled.
Also, the realisation that the "speed of light" is denoted as c (causality, anyone? ;) ) made me smile :)
Travelling at c, your perception of time would have stopped. From that point, it can't become more stopped, any more than you can go faster.
ADVICE FOR BLACK HOLE EXPLORERS
The only way to get out of a black hole is to not go into it.
If you're planning to go into one, don't. You won't be able to get out.
If you do go into one, the only way out is to reverse time until before you went in, and then don't go in.
Past a certain point, the distortion of spacetime becomes so great that no speed attainable can overcome the effect of it dragging back. So even travelling at the speed of light, you couldn't go faster than the gravity treadmill speed pulling you back in.
For clarification - gravity is nothing like a treadmill. It just happens to work nicely as an analogy for this.
So these claims, you could escape a black hole if you travel faster than light speed, should be read as, if we use our Euclidean sensibilities in a Minkowski setting,... It is in some technical sense correct, but without the technical details meaningless.