In a pure gravitational field, the time-dilation effect also creates a practical barrier to access to the universe at large once the dilation is large enough. For example, you could take a hyperbolic orbit approaching close to the event horizon of a sufficiently large (mega-sun) hole to travel far into the future in the sense that the trip is short for you and the ship -- but arrives far into the future of the external frame. One issue is that in the portion of the trip close to the horizon, all the light that falls on you for the external length of time occurs blue-shifted in the local frame you probably are blasted by cosmic-ray energy photons which were starlight in the 'slow' external frame.

To arrive at a time-point before you left, requires a very rapidly spinning hole and seems to require crossing the event horizon. Although such a trip can miss the singularity, it is not clear where you end up in that there is no guarantee that it is in this universe unless our space-time is multiply connected.

There are other approaches to time travel which might not require and event horizon -- check out 'Tipler' machines... still not practical, but quite interesting.

Hello! I will try to help you:
In fact, you are quite right; creating a super large gravitational field is the only way to do this. You can never accelerate up to the speed of light, and you certainly can't travel faster! First of all, Einstein's equations of special relativity tell us that to reach the speed of light, you would need infinite energy. Since this is impossible to achieve, we can't do it. Photons have zero mass. So, the other way to do it is by folding space-time with a large mass- this is essentially what a wormhole does.

You get two black holes to poke through space-time to create a worm hole, and you have a time machine. The only problem is, since gravity warps space-time, if you could create a wormhole, once you go into it, your small mass would cause it to collapse!

Now, suppose you had the technology to create a wormhole AND keep it open; if you go back in time, you will alter your own future, and then what would be the guarantee that you would even exist, so you could not have gone back in time. This is what we call a paradox.

Stephen Hawking has come up with a solution to this paradox: if you went back in time, you could not return by the same path. You will alter the future, but not your own future. You would be the only one to remember what you did. Problem is no one in the new future would believe you.

A good reference about time warps and black holes is by Kip Thorne; I forgot the exact title, but if you look for Kip on Amazon, you'll find it.Lawrence Krauss has also written about this in his book, The Physics of Star Trek.

There is currently no known way that you can go backward in time using either high speed or gravity. As you said, you can almost (but not quite) stop time if you're traveling at velocities close to C, or in the bottom of a huge gravity well. But neither of these can actually stop time, much less go backward in time.

If time travel is possible, it will likely require either worm holes or some kind of futuristic "warp field" that suspends the laws of physics as we know them. We obviously don't know of any way to use either one of these right now. In fact, if worm holes exist at all, they are apparently smaller than a single atom; we've never detected one. Most theories of worm holes rely on the existence of some kind of exotic matter with negative energy density, and this has never been observed in practice.

One humorous "proof" that time travel will never work was the MIT Time Traveler Convention back in 2005. The idea was to hold a big party which future time travelers would know about, hoping they would go back in time and visit it. But no one from the future showed up. (Or at least they weren't seen. Maybe they had invisibility cloaks and wanted to avoid all the questions.)

The problem with trying to go faster than light is that any object with any finite mass will become infinitely massive as it approaches the speed of light, and therefore require an infinite amount of energy to actually get there. If you somehow could get there, then going even faster would result in your acquiring an imaginary mass (because the equations of special relativity result in taking the square root of a negative number if your velocity is greater than c).

The formula is:

M = m/ √(1-((v/c)²)) , where M is mass, m is mass at rest, v is velocity, and c is the speed of light.

Being in any gravitational well will cause time to slow down, but it won't stop time unless the well is infinitely deep (i.e. the singularity at the very center of a black hole), and it certainly won't reverse it. There is a formula for this, but it is general relativity, and I don't understand the math well enough to explain it to you.

So far as we know, there is also no way to create an artificial gravitational field.

Now, there was a recent article in the Science magazine that announced that some mathematicians have figured out that it is possible in theory to use a spaceship moving in a certain way to create a gravitational well that could propel the spaceship back in time. I don't know how this works or what the limitations on it are (e.g. the spaceship might need to have the mass of a galaxy or something like that). But there is the idea, at least.