How exactly does time slow down near a black hole?

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                   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.

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.

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.

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