How can I get rid of gnats without hurting my pets?

I have pet rats, and I'm not sure what attracted them, but a bunch of little gnats appeared around their cage. I cleaned their cage today and I don't have any trash or rotten anything nearby, the cage is in my bedroom, but the flies are still there. If I still have this problem after 24 hours, what can I use to get rid of them? (PREFERABLY without pesticides or chemicals) Without calling an exterminator?