Black Holes
As I mentioned before a black hole is an object that has all of its mass within its Schwarzschild radius. For densities that high the gravitational force overwhelms degenerate electron and degenerate neutron pressures. Beyond this there are no known pressures that could support the matter against the force of gravity. Gravity crushes all of the mass into a point, called a singularity, of infinite density. The spacetime curvature inside the Schwarzschild radius is infinite (see figure 2).
Figure 2: An Embedding Diagram of a Black Hole
The surface at the Schwarzschild radius is called the event horizon. Crossing the event horizon is saying goodbye to that region of spacetime forever. The possibility of backward time travel is due to the possibility that the black hole may empty out into another region of spacetime. Another region of space and another time, possibly the past.