Some zones in Magic belong to a single player, like a player’s hand library and graveyard. However other zones, like the battlefield, stack and exiled zone are shared. When a permanent in is in the battlefield, it does not matter if it changes controller it will remain in the battlefield. Objects in play do not move from one zone to another when they change controllers, even though they are often moved around to show which player controls.

This matters as abilities that trigger when a permanent enters the battlefield or leave the battlefield will not trigger. For example, the enters the battlefield triggered ability of Acidic Slime will not trigger when it changes controler due to a Act of Treason.