Relativity and acceleration-acceleration To save expert's time: "In GR, is jerk relative?"

As I understand it, "Special Relativity" applies only for (in a word) objects which are not accelerating.
Einstein thought about this hellova' hard for some years and came up with General Relativity:
which covers the case of objects (in a word) accelerating.
So - that's the first two derivatives of position covered.
The third derivative of position is usually called "jerk".
Much as Special Relativity fails with acceleration, in fact, does General Relativity fail with the next derivative, and the following derivatives?  What's the situation here?
(Don't even mention circular movement - does this cause extra-special problems when you have, perhaps, higher derivative change in circular motion?) Cheers.
 A: You understand wrongly I'm afraid.
It's commonly said (by non-relativists) that special relativity doesn't describe acceleration but this is quite incorrect. Accelerating frames can be described perfectly well by special relativity. As an example look at my Q/A How long would it take me to travel to a distant star?. This analyses the motion of an accelerating spaceship, and it does it just using special relativity - no GR to be seen. Alternatively look at the last part of my answer to Is gravitational time dilation different from other forms of time dilation?, which analyses circular motion (i.e. acceleration towards the centre) again using just special relativity.
So I'm afraid your argument that jerk might cause GR to fail is based on an incorrect premise. Both SR ad GR can handle jerk and all higher time derivatives of acceleration without failing.
There is a fundamental difference in the way SR and GR treat acceleration because acceleration is absolute in SR but relative in GR. However this is unrelated to the issue you're asking about.
A: General relativity describes measurement and observations for a general observer.  Theoretical problems with it lie mainly in its interaction with quantum mechanics and statistical mechanics, and there are no experiments that disagree with its predictions.
