There's no love lost between Kevin Costner and his ex-wife Christine Baumgartner ... who finalized their divorce earlier this week after six bitter months when Christine challenged the prenup she signed ahead of their 2004 wedding.

But matters regarding prenuptial agreements can get tricky really fast -- something our own Harvey Levin digs deep into on "TMZ Investigates: Kevin Costner's Divorce War", airing on FOX Monday at 9/8c on Fox and the next day Hulu.

As you can see from the clip, HL and celeb divorce attorney Chris Melcher dive into the prenup world by role-playing as an engaged couple. Chris lays it all out ... explaining he must have a prenup in place so they both understand their financial expectations and know their marriage will be protected.

HL fires back ... saying he's entitled to half of what he earns simply 'cause they're partners -- adding their contrasting views on the matter means he doesn't truly love him.

But Chris ain't budging ... saying if things were to go south, he'd want peace of mind that things wouldn't get messy. In fact, he feels so strongly about the matter he tells HL an open-ended deal means he'd call off their wedding entirely.

But as we all know, even though Christine signed a prenup with Kevin, things quickly turned acrimonious between the pair as she asked for an eye-popping $248,000 a month after filing for divorce -- listing $100,000 for cosmetic surgery as an expense declaration. She ended up getting $63,000 a month in child support.