Where do I find the rift pit to toss your pet into? And does your pet stay a rift pet afterwards? It doesn't change back? I want a rift pet but unsure how to do so. Thanks!

Here's the rift

If you toss your pet in, it'll stay gone for a few days, then come back turned into either a riftborn pet, or, if the pet doesn't come in that color yet, one of two rift creatures. You can see all the riftborn pets here

Edited to remove my redundant info!

thanks!