Mariah Carey made sure the world knew she was singing live onstage in Central Park for “GMA” yesterday. We’re told the superstar wanted to avoid any lip- synch scandal after she was accused of doing so on the recent “American Idol” finale (which she denied). A source tells us, “Mariah wanted everyone to know she was singing live.” In fact, she put so much effort into her performance, she split the back of her tight, pink Versace dress, forcing her to hold onto the front to maintain her modesty.