Cut a hole in the door to fit a fan, setup a box around it, cut a hole in the box and attach a carbon filter to it so the air gets pulled through the filter and pushed out the door, screw in a vent cover on the outside of the door to make it look like a normal vent, the box built behind the door will block light so you won't have light leaking out. With this setup the air being pushed out of the room will make a vacuum and will automatically suck air in under the door. If money is an issue get a cheap 10 - 15 dollar desk fan thats quiet and you can get carbon filters that are made for air purifiers for about 5 dollars on amazon and use a cardboard box as the box built around the fan. The setup works for a closet grow and is very cheap, I have only spent about 30 dollars on my materials for my exhaust.