Answer 1:
Actually, the answer to this is not so
complicated. The reason it appears to be a unique
feature of Black Holes is that the effects are
very pronounced in that case, but changing of time
is an everyday event, throughout the universe
(i.e. even in your own back yard...).
Suppose you toss a ball into the air and inside
the ball is another ball. If the outer ball was
being acted on by a force, it would move 
pushing against the inner ball. Yet, somehow, when
gravity pulls on the outer ball, is also pulls on
the inner ball with just enough force that the two
balls accelerate together. This is a fairly
unlikely scenario given you don't know the
composition of the balls or that you could change
the mass (and hence the force) easily for one of
them.
Einstein didn't like this notion either  and
came up with an idea: he claimed that the force
of gravity is nothing more than an
acceleration, so that the force you feel in an
elevator is really just gravity, not gravity plus
some other force. In this picture, a falling
elevator (in which the objects inside feel no
force) is indeed not under the influence of a
force, despite the fact it is accelerating
relative to the building it is in. On the other
hand, he would argue that a 'motionless' elevator
does sense a force, as every object in it is
mashed to one side by the acceleration. This
broadly described the principle of equivalence
between an accelerating frame and a frame under
the influence of 'gravitational force'.
How can a body which is not moving be
accelerating? Remember that acceleration is
defined as change in velocity with time or change
of change of position with time. Here if
position is constant, it would appear that
acceleration is zero. However, what if TIME was
passing at a different rate (slower) closer to a
large massive body (like the earth). In that case
you would still have acceleration, without motion,
and if you had no acceleration, you'd have to be
moving (falling). This is precisely what is meant
by time moving slower  time really is moving
slower closer to the surface of the earth than in
orbit and gravity is the consequence of this
behavior. The reason that you don't notice time
moving slower, is that there is a pretty large
constant setting the time scale from the distance
scale  the speed of light (~300,000 km/s).
Because of this, over distance scales of a inches
or miles, the shift in time is very, very small,
but is still significant as you have seen.
(objects which are not accelerated tend to quickly
move this close to the earth).
>Close to a black hole, the acceleration
gradient is very much higher  so much so that
the difference in time delays becomes infinite as
you approach the surface. If the hole was large
enough, you could even survive the gradient
(tides) due to the difference in time speed
between your head and feet. If the earth was
packed into a black hole, all its mass would be
packed into a ball about a cm in diameter  you
can try to imagine the tides from such a source.
As it happens, by many experiments, (even
flying atomic clocks in orbit), these effects have
been observed and validated, so this theory is
working practice. Always, remember, however, it is
only one step closer to the truth, and will be
revised when better models and theories are
validated.
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