How exactly does time slow down near a black hole? How exactly does time slow down near a black hole? I have heard this as a possible way of time traveling, and I do understand that it is due in some way to the massive gravity around a black hole, but how exactly does that massive gravity slow down time?
 A: This web page provides a good explanation.
To oversimplify the explanation, you have to understand the curvature of space time around a black hole.  The basic principle is that because of the curvature of spacetime around a black hole, the amount of "distance" a beam of light has to cover is greater near a black hole.  However, to an observer in that gravitational field, light must appear to always be 300,000 km/sec, time has to slow down for that individual as compared to someone outside that gravitational field as related by the time/distance relationship of speed.
Or as the web page says:

If acceleration is equivalent to gravitation, it follows that the predictions of Special Relativity must also be valid for very strong gravitational fields. The curvature of spacetime by matter therefore not only stretches or shrinks distances, depending on their direction with respect to the gravitational field, but also appears to slow down the flow of time. This effect is called gravitational time dilation. In most circumstances, such gravitational time dilation is minuscule and hardly observable, but it can become very significant when spacetime is curved by a massive object, such as a black hole.
A black hole is the most compact matter imaginable. It is an extremely massive and dense object in space that is thought to be formed by a star collapsing under its own gravity. Black holes are black, because nothing, not even light, can escape from its extreme gravity. The existence of black holes is not yet firmly established. Major advances in computation are only now enabling scientists to simulate how black holes form, evolve, and interact. They are betting on powerful instruments now under construction to confirm that these exotic objects actually exist.

This web page provides a large series of links for further research into the subject:  http://casa.colorado.edu/~ajsh/relativity.html
A: According to wikipedia the time as measured by a clock will slow down (as measured by a far away observer) by a factor 

In which G is the gravitational constant of the universe, M is the mass of the black hole, r is the distance from the black hole to the clock.
That is exactly how it slows down.
A: A good analogy for the strangeness of space and time around a black hole is traveling from the US to Canada. You feel about the same and the surroundings look the same (like nothing special happening to you when you cross the black hole's event horizon), and the prices in the stores look about the same, but if you try to use the money you brought with you, you suddenly have to make these non-local corrections. Likewise, your own personal time always "feels" the same when you explore a black hole, but your clock runs slower than someone else's clock that is farther from the black hole.
And in fact, crossing the black hole's event horizon is the equivalent of changing your money over to (worthless!!!!) Zimbabwean dollars- your clock seems to stop entirely, from the point of view of someone far from the black hole, even though things seem just fine from your own point of view.
PS- A black hole can be used only for time travel into the future! Just hang out close to the event horizon for a while and then return. Much more time may have passed for everyone else because your clock seemed to run so slowly.
A: Time slows down near any massive body; black holes are merely the most extreme example.  GPS satellites orbiting the Earth have to correct for the fact that time passes very very slightly more slowly on the Earth's surface than it does in geosynchronous orbit -- by about one second per every 60 years.
In a sense, gravity and time dilation are the same thing: they are both consequences of the curvature of spacetime near a massive body.  You can't have one without the other.
A: Time indeed slows down around a black hole according to Stephen Hawking. Now this phenomenon happens because of the super gravitational force of the black hole. By virtue of this enormous force the black hole warps the space-time present all around it to such an extent that time around it slows down considerably.  You may imagine that due to its attractive force the black hole would hold down the space-time so close to itself that even flow of time slows just because the black hole has bent the fabric of space-time so much.
A: Consider the question: Time slows down? Do we know what is time? That is the first problem. Without going into details consider this definition: "Time is presence of motion and forces." 
This definition is derived as follows: Consider two masses orbiting around each other held together by a force. Now imagine that time slow down in this system. You expect slowing of motion. What about forces between the two masses they should weaken at the same rate to keep in the same orbit. If the time and motion stopped completely the force should disappear. 
Now the next question is where does time come from or how is it produced? We live in an expanding universe and time is slower near intense gravity where expansion of space is slower. So time is related to expansion of space or caused by expansion of space. So around neutron stars and black holes expansion of space is slow causing slowing of time. You may ask why does time slow with motion?  Well if total motion allowed by expansion of space is constant then if you increase the external motion of a mass then internal motion slows down. This we seee as slowing of time. 
A: I know that black holes are formed by the collapse of stars and a black hole has an enormous attracting force. The gravitational pull is so powerful that even light cannot escape. As we all know, gravity also affects light. So, due to gravity, time slows.
