hmm The argument for and against time travel is very interesting. Einsteins theories of relativity seem to allow for time travel however Stephen Hawkins string theory seems to rule it out. Einstein's theory says the faster an object moves the slower time passes for that object in relation to the stationary observer. His theory goes on to state as you aproach the speed of light time indeed sslows and stops, once the speed of light is achieved. Indeed his theory seems to point to the possibility that if the speed of light is surpassed time would start going backwards for that object. (theory of special relativity)
Hawkins on the other hand postulates that the speed of light is finite , therefore time can never go in reverse. He also theorizes that in order to manipulate time,you would need a region where a weak energy condition is satisfied, meaning that the region contains no matter with negative energy density (exotic matter)
Hawkins explainanation is addressed in his 1992 paper on the chronology protection conjecture, where he examines "the case that the causality violations appear in a finite region of spacetime without curvature singularities" and proves that "[t]here will be a Cauchy horizon that is compactly generated and that in general contains one or more closed null geodesics which will be incomplete. One can define geometrical quantities that measure the Lorentz boost and area increase on going round these closed null geodesics. If the causality violation developed from a noncompact initial surface, the averaged weak energy condition must be violated on the Cauchy horizon."
By the way do not concern yourself to much with the mathamatics involved just concentrate on the explanation. I am a medical radiation physicist and I to have a hard time with the mathmatical argument Hawkins proposes .