How can you use black holes for time travel?

Black holes can be used to travel into the future only. So far as we know, our universe prohibits traveling into the past.

According to Einstein's theory of general relativity, and to experimental evidence here on earth assembled by Harvard physicists Pound and Rebka, in the presence of a gravitational field, an external observer would see a clock in a strong gravitational field tick more slowly. This is analogous to the famous time dilation effect in special relativity, except that in the 'gravitational redshift' effect no motion between the observer outside the gravitational field and the clock located within the field, is required.

What this means is that if you were traveling into a strong gravitational field and sending out pulses of light every second, an observer watching these signals from a great distance would see the interval between the pulses increase from seconds to minutes and then hours as the field got stronger and stronger.

Black holes are fantastic sources of very strong gravitational fields. What a distant observer would see as your clock got closer to the so-called Event Horizon of the black hole is that the pulse interval would increase without limit from one second to one month and longer. The frequency of the light pulses would also get longer as the light lost more and more energy struggling to get out from the vicinity of the black hole. As your friend finally entered the black hole by passing across its event horizon, the last photon capable of making it to infinity is emitted at almost infinite redshift, meaning that if you originally emitted a gamma ray with an energy of 1000 billion electron volts, buy the time your friend received it far away, it would have lost enough energy to become a radio photon with an energy of 0.00001 electron volts! So, if it took your friend 1000 hours to travel from where you are to the black hole, the last photon he sent you just before entering the black hole, would arrive at your location 1000 hours from now, but when you looked at the interval between the last two pulses he sent, you would see that they are not the one second interval you started out with, but say 1 or 2 minutes or more. But here's the rub. According to your infalling friend, he/she is still sending the pulses out once each second!

In other words, one second to your friend falling into a black hole is several minutes to you and, in essence, your friend is aging more slowly than you and is traveling into the future faster than you are. If he/she could manage to put on the breaks just before crossing over the Event Horizon and escape to rejoin you, you would note that his/her clock reads a much earlier time than your clock. To your friend, only 2000 hours may have elapsed, however, YOUR clock would read perhaps 10000 hours or several weeks have elapsed depending how close to the Event Horizon your friend could get before escaping. The tidal gravitational forces are enormous near small black holes the mass of the sun, so your friend would be shredded into spaghetti within a few hundred miles of the Horizon. For supermassive black holes of several billion solar masses, however, the tidal forces near the Horizon are very small and survivable. This means you could accidently find yourself passing across this one-way barrier, and only realize your mistake when you tried to escape and found it impossible.

In principle, if you could get within a few millimeters of an Event Horizon before escaping, you could essentially time travel years or millenia into the future as measured by outside clocks. According to your clock, however, perhaps only a few hour or days actually elapsed.

Note, all of the above numbers are pretty darn approximate and are given to qualitatively show the magnitudes of the effects.