Can two colliding black holes create a region where time goes backward?

[michojek]

I was just reading upon black holes, collision and how it bends space and time..
I know for a fact that time stops after the event horizon, but during the collision of two black holes, can the gravity 'overlap' between them to make it strong enough to bend space which in result be enough to have the region of space go back in time? (sorry if it doesn't really make sense)

 

[PeterDonis]

I know for a fact that time stops after the event horizon

No, you don't know that for a fact, since it's not true.

during the collision of two black holes, can the gravity 'overlap' between them to make it strong enough to bend space which in result be enough to have the region of space go back in time?

No.