The way that you play in this situation should not be the same in all cases - and a lot is read dependent. A lot has to do with how the table has been playing since you got shorthanded - has there been a lot of undefended blind stealing, lots of open raising or has it been rather passive with lots of calls and folds? This has a big impact on how you play at this point - it's not JUST about the cards even though you have a great hand here.

In this case I'd probably not push, but rather come over the top with a raise of about 40% of my stack, or 2k. This basically states the same as a push, that you have a strong hand and you're willing to commit to the pot with it. The problem I see with a push is that you're only getting called by a hand that is willing to race - perhaps another big ace that you have dominated but also perhaps a small PP. You're limiting the hands that will call your bet to a select few that you beat badly or the hands that are ahead of you preflop. I think that a reraise is a better way to get more chips out of your opponent and might even get them to push into you thinking you're just on a resteal.

There are honestly a lot of different ways to play this hand in this situation. This is just one way that, in my opinion, has a good chance of being called and extracting more chips out of your opponent.