What happens when you have infinite energy?

[Lord Torath]

It still being there a few days after waves stop transfering energy into it.
You know, long enough to destroy a star system with a spacetime Eddy.

To further clarify, do you mean using gravity waves to compact material tightly enough that it forms a black hole? In such a case, the black hole will be as stable as any other black hole of its size.

Or focusing gravity waves so their pull is as strong as a black hole? In which case: see factotum's reply.