Event horizon
Don't forget that for an infinite Mass, the event horizon is infinite in extent.
For lesser masses, the time compression associated with even horizons has already been addressed by serious scientists. I can't find an URL but it must be out there somewhere waiting for a web search.
Remember that Lorentz time compression is asymmetrical. An observer sees you burn up in milliseconds, while you get to live out your normal lifespan before final impact... (or something like that, IF you can survive the huge gravitational gradient trying to stretch you and your spaceship like a piece of spaghetti)
