If you were in an Alcubierre drive bubble travelling at exactly 1 c, I wonder what it looks like if you looked back, to the direction you come from. If you went faster-than-light you'd obviously see nothing behind you, just pitch black. When travelling at 2 c, I think that the visibility border would be 90 degrees to your sides. But if you went at 1 c, the light beam that reached you from behind is still with you, so does it look like if time was frozen behind you?

I know that when travelling near, at, or above light speed the stars before you would turn blue and the ones behind you red, if still visible. I guess the faster you'd fly the more would the colors shift, until the stars before you appeared red, while close to and behind you nothing would be visible.