What happens when you have infinite energy?

[Anymage]

So, could you make a stable black hole out of gravity waves? Just asking for a friend.

In theory anything with enough energy could form an event horizon, so yes.

In practice, even an arbitrarily advanced society would have much more effective ways of making a black hole if they wanted one. Even in a sci-fi setting, I can't see why anybody would do this unless you're just looking to spruce up your technobabble and don't care overmuch about the real-world meanings.