Time Travel Mathematically Possible
The Alcubierre drive was theorized by Mexican physicist Miguel Alcubierre in 1994. The hypothetical warp drive envisioned that a spacecraft could achieve faster than light speed travel, basically warp factor 5 and beyond. In the Alcubierre theory, a spacecraft would traverse emmense distances by contracting space ahead of it and expanding space behind it which in effect would create a vortex in which a vessel could travel faster than light.
The theoretical Alcubierre drive would require a hull of exotic matter to transport passengers at super light speed and hence travel through spacetime. The proposed Alcubierre drive calls for a negative energy density which requires exotic matter that is also theoretical, it's existence is only theorized and not proven. So if this exotic matter can not be located, or does not exist, then the theoretical spacetime warp drive could never be constructed.
More recently, 2017, two physicists, David Tsang [University of Maryland] and Ben Tippet [University of British Columbia] published a paper in 'Classical and Quantum Gravity'. They believe that they have devised a mathematical model for a theoretical time machine. This time machine they claim is a vessel, in this case a box, that can be moved through time in either direction forward and back. They dubbed their theory Traversable Acausal Retrograde Domains in Space-time [TARDIS].
The methodology they propose is similar to that proposed by Alcubierre. They speculate that the curvature of space-time in the Universe can be used to bend time into a circle for passengers sitting in their envisioned box. Once within the circle travel to all points past and future are possible.
Einsteins relativity ties the gravitational effects observed in the Universe to a natural curvature in space-time. The phenomenon is believed to be the cause of elliptical orbits of planets and stars.
If the world were flat as some would have us believe, space-time would be uncurved and celestial bodies would move in straight lines as opposed to the circular rotations and orbits we see. As per Einsteins relativity, the geometry of space-time curves in the vicinity of higher mass objects, which causes planets to bend their paths and orbit around their suns.
Traversable Acausal Retrograde Domain in Space-time [TARDIS] postulates that not just physical space, which is the dimensions our consciousness perceives can be bent and twisted in the Universe but time itself, which is effect is the 4th Dimension can also be curved in the vicinity of high mass objects.
Tippett stated "The time direction of the space-time surface also shows curvature. There is evidence showing the closer to a black hole we get, time moves slower..."
To capitalize on this theoretical property of the Universe, a 'bubble' in space time would be created and carry its occupants along an eliptical path through spacetime.
If this bubble/ vessel/ box attains greater than light speed which is mathematically possible as per the thesis, travel through time [spacetime] would be possible. Although it is mathematically possible, at present it is still not feasible to construct this device because the material necessary - exotic matter has yet to be discovered, we are not certain if it does exist.