Hey found a bigger battery but it still fits like the regular s3 battery. The question is to actually see if there is any improvement. I got it in the mail today its a 2900 mah instead of a 2100. It still fits the same and i don't need a special back for it. Im gonna drain it to 0% then charge it fully (Think that's what im supposed to do the first time.) Then ill see if it last better than my stock battery. Here is the link it was cheap and comes with a wall charger!
New 2900mah Battery + Charger for Samsung Galaxy SIII S3 i9300/T999/i535/L710 | eBay
New 2900mah Battery + Charger for Samsung Galaxy SIII S3 i9300/T999/i535/L710 | eBay