Can Black Holes Enable Faster-Than-Light Travel?

[Toms]

first, I would like to apologize for my lousy english
second,I hardly know anything about relativity (well I understand why you can't travel faster than light, and i understand a few concepts,so I get the simplfied big idea , but I don't know the fine stuff of it)
me and a friend were discussing f.t.l traveling yesterday.
We have read about faster than light traveling by taking a shortcut through space time
now so far evrything I have read is about light that travels in a straight line
but what if light is bended (by the gravity of an extremely dense object, for example, a black hole)?
i made a picture of this

http://img72.imageshack.us/img72/8672/ftltravelispossibleun7.jpg

now thanks to the black hole, the light is not taking a direct way from point B to C
and traveling more distance.
Assume you would counteract the gravitational force of the black hole by igniting side rockets, so you *DO* go in a straight line
faster than light travel mean : basically traveling faster than light, so in this example
is it true that you are traveling faster than light?
or are we horrible wrong here ?

 

[atyy]

In general relativity, it makes sense to say that we cannot travel faster than the speed of light, and also that we can - each meaning something different.

In special relativity, which applies when there is no gravity and space is flat, we can draw space as a horizontal axis and time as a vertical axis. Then the spacetime path of a ray of light will be a straight line with a certain slope. A spacetime path with a slope less than than that of the path of light, represents a particle traveling faster than light, which is forbidden.

When spacetime is curved, only very small parts of space are approximately flat, and within any small region of space, nothing can travel faster than light in the sense defined above.

For large curved regions of space, the above definition no longer holds, and the meaning of the speed of light is ambiguous.

Here is an article describing the different definitions of the speed of light in curved spacetime:
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html