Verified answer

This isn't a direct answer in that I don't know how Godel manipulated Einstein's equations. But I have another answer from a philosophical perspective.

Godel may have manipulated Einstein's equations successfully, but that would prove time travel possible only insofar as the equations accurately described the real world. Physicists, and scientists in general, often apply mathematics to phenomena without being sure they understand what they are applying it to. A good example is the term "speed of light." The uniform measurements of Michelson-Morley led to special relativity, but noone bothered to notice that the term "speed," or to be more scientific, "velocity," was developed in physics to describe the mechanics of physical objects. If you measure light's velocity, you are assuming that light is something that can move in the way objects and material waves move.

Likewise, physicists in measuring time have often regarded it as though it were another "dimension," which is a word initially used to measure space in the simplest way possible. Regarding time as another dimension essentially posits a larger "space-time continuum" for which an extra dimension is necessary for accurate measurement.

Unfortunately the "4th dimension" doesn't resemble the other 3 very much. The 3 dimensions of space are all the same type of measurement (what the concept of dimension is based on, remember), but the measurement of time is very different from the measurement of space. the measurement of time was originally based on comparing spatial measurements, and setting standards based on repetition of a physical movement (i.e., the sun crossing the sky)

The idea that the sun is moving [i]through[/i] something (besides the sky) is a convenient way to visualize this measurement, but it does not explain just what this something is, as it can not be directly observed.

In addition, since the concept of time was based on the movement of objects in space, to posit that objects can move through time as they do through space simply invites the imagination to measure such movement through time as well, and posit such measurement to be a 5th dimension which also can be moved in as through space. And if so a 6th dimension could be posited measuring movement through the 5th.

In general, I think it is foolish to assume that time is the kind of thing that can be "moved through" in the same way that space is, simply because of the convenience of this visualization in describing observed phenomena.

Thus I would give you a Wittgensteinian answer: what do you mean, time travel? I know what space travel is, but if you mean "backwards in time," I'd suggest you'd be confusing yourself into a bad usage of the word "backwards," the same way physicists have confused themselves with the phrase "velocity of light."

There are several famous physicists who have suggested possible means of time travel. But all of these means of time travel have involved physics that was not well at the time and this forces them to make assumptions about the behavior of the universe. For instance some modern "theories' of time travel rely on Tachyons and wormholes. There is no experimental evidence to suggest that either exists, they are theoretical objects. The same is true of what Godel did. In solving Einsteins equations he made certain assumptions about the behavior of the universe that turned out to be false.

No idea, but I´ve got another way to time travel... in brasil it is four hours earlier than it is with me....