Blender

A scene i'm trying to make includes a hole in the sky that i'd like to have disintegrating edges, as shown here. I should only need one angle on this scene so i don't need something that's pretty from every angle.

Here's what the scene looks like currently, with a filled black circle for the hole.

And here's roughly what it should look like.

I used GIMP's pick and blur filters to do this, but i'm curious to know if there's a good way to get this same effect straight from Blender. What are my options here besides editing the picture every time i update the scene?

Thanks in advance.