Kerr's Black Hole
If the black hole that we followed Chris into had been a rotating black hole then it would have been described not by the Schwarzschild metric but instead by the Kerr metric. I will not clutter the page with its mathematical form because it would take far too much explaining to get to a simple result. The critical change that occurs in the black hole, besides its shape and number of surfaces to pass through, is that now the singularity can be avoided. Some think that black holes may dump their matter into another spacetime region through objects called white holes. They would be the exact opposite of black holes. Instead of having an event horizon there would be an anti-event horizon through which matter can only leave but never enter. Black holes have never been directly observed, as that would be all but impossible. There is observational evidence for their existence by their gravitational influences on nearby objects. However, no one has ever observed an object that could be a white hole, so their existence must be called into question. If they do exist it is possible that they do not empty into our universe but rather into another universe altogether. There are still some problems with this time-machine. If a white hole did exist the anti-event horizon would be very unstable. A single photon of light that fell upon it would grow more blue-shifted and gain so much energy that it would convert the anti-event horizon into a regular event horizon within a fraction of a second of the white hole's creation. This would trap us inside yet another event horizon before we ever had a chance to escape through the white hole. There are additional arguments to show that a black hole would not be traversable. But I think it has become obvious that black holes are a lost cause as far a making time machines is concerned.