Is There a Limit to How Much Space-Time Can Curve?

[Crazy Tosser]

First I thought

If nothing can move faster than c, then nothing can accelerate faster than c/sec, right? Well, that means that the maximum amount space-time can curve is up to the ol' 45 degree slope, not like straight down as some black-hole pictures are made. Right?

And then I thought

If the space-time curvature exceeds c/sec, there is an event horizon formed, and no information from that area can reach us - no light can escape that place, and thus the postulates of relativity are not violated.

And now I am confuzzled

 

[Dale]

If nothing can move faster than c, then nothing can accelerate faster than c/sec, right?

No. What would make you think that? We get much greater accelerations in particle colliders, and probably even in x-ray tubes.

 

[Crazy Tosser]

I was actually just going to post again that I realized that this acceleration would have to continue for one whole second >.< If a mod can please lock this sign of my stupidity>.<

 

[daytripper]

What if a planetary body was so massive that the acceleration 299,792,458 meters from the surface was 1c/sec. That would give the mass enough time to accelerate to c, right? I don't know, this is just idle speculation. The thread peaked my interest.

edit: It would accelerate far past c (in classical physics, at least), as the acceleration would increase near the surface