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Gravity is like a pillowy soft matress. If you drop some light objects on the matress then one really heavy one, you'll notice that the heavier object will create a big bend(distortion). Following that, you'll see that the closer(lighter) objects will be pulled towards it. So, heavy objects in space distort the space-time continuum. If you can successfully exploit space-time then you can possibly travel through time.

Black holes and worm holes(smaller black holes) distort space and time greatly. *Black holes are holes in space and time. It is a concentration of matter so dense that the gravitational feild created by it cannot be escaped,not even light. Black holes bend gravity until it rips. Einstein and nathan rosen developed an idea, that a black hole might be connected to another rip in another black hole,joining two disparate parts of space-time by way of a narrow channel. It is believed that black holes are short cuts through space and time

One method of time travel is to put an anti-gravity device within the channel of the wormhole in order to allow a space craft to travel safely through it. The channel linking the two worm holes, is smaller than the center of an atom. So the anti-gravity device  enlarges the channel enough to allow access for a spacecraft. Also, anti-gravity keeps the space craft form being torn apart by the black holes' vast gravitational power.

Another method incorporates theory of cosmic strings.  J. Richard Gott III suggested that these  hypothectical objects might permit travel backwards in time. Cosmic strings are extremely dense, infinitely large, and no wider than a single atom. Theory goes that if two comsimic strings that are parallel,  whiz by each other at the speed of light, they would greatly distort space-time. If  nearby astronauts exploit this at the right time, then they should be able to end up at their starting point before they even left.
PARADOX
If you were to go back in time and  kill one or both of your grandparents,then that would mean you would never have been born. So how could you've possibly made the trip to go kill them?
THE MYSTERIES OF TIME TRAVEL
Lightning travels around 87,000 miles a second.
When objects are travelling exrtremely fast, or passing by a massive object, time will pass by slowly.
Light travels around 186,300 miles per second in the vacuum of space and only 140,000 miles per second  in water
Nothing can travel faster than the speed of light within a vacuum. Only through materials.
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SOURCES: Popular science:micheal moyer, *The complete idiots guide to understanding einstein.