This turned into a great discussion. j.d. has made all of the points I might have...probably better than I would have.
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time cannot be turned back on itself, nor created before it exists, without involving the whole
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This was, in essence, what I was thinking when I said what I did.
As for black holes, going by current theories, you might be more likely to end up in another, parallel universe than time travelling as we normally think of it (assuming that you survived). Braneworld theories conceptualise our universe as a 3-D 'membrane' to which all of our fundamental forces and particles of matter are 'tied'.......except gravity. The membrane exists in a fourth large spatial dimension called the 'bulk', which contains other membranes...other universes.
All of this has emerged from string theory, and what makes gravity different is that its strings (gravitons) are closed loops, so they can 'float off the membrane'. This has led some cosmologists to suggest that the extreme gravitational conditions inside a black hole might make it possible to contact or even move into (ignoring the fact that it would probably kill you) an adjacent universe. For the time being this is highly speculative.