Is it possible to make a machine through which we could travel both in the future and the past?

Hi RAB,
Celebrities figured time travel a long time back! Look at these snaps of them long before and now.
Just kidding! Jokes aside, many have dreamed of figuring out how to travel in time—and dismissed it as impossible. Now, researchers have proposed a mathematical model that makes time travel possible, using concepts of Einstein’s theory of general relativity coupled with the hypothesis that time is not a separate dimension.
Traditionally, we think of the universe as being made up of three spatial dimensions, and a fourth dimension representing time. But mathematician Ben Tippett at the University of British Columbia, Canada, says this is wrong. He believes time should not be separated from other three spatial dimensions—instead all four run together, simultaneously.
Working with David Tsang, an astrophysicist from the University of Maryland, he has worked out a way to use this principle to make time travel possible. Their findings have now been published in the journal Classical and Quantum Gravity.
“People think of time travel as something fictional,” Tippett said in a statement. “And we tend to think it’s not possible because we don’t actually do it. But, mathematically, it is possible.”
He explained how the time machine—Traversable Acausal Retrograde Domain in Spacetime, or TARDIS—would work. In general relativity, the curvature of spacetime causes gravity by exerting a force on objects passing them. These curves cause planets to orbit stars—if spacetime was not curved, all the planets and stars would travel along straight lines. So if spacetime is curved, and we run time along it simultaneously, then theoretically the bend can be turned into a loop, making time travel possible
But will such a machine ever exist? Tippet says no. “Our paper included a careful analysis of this geometry, and the problems it would have in being built,” he says. “Generally speaking, backward time travel usually causes singularities (places where there are holes in the universe) or instabilities which would cause them to collapse into a black hole if they get poked the wrong way. So unfortunately, I don’t foresee this as being feasible."
So, there you go. In this universe it is not possibe, but maybe in another parallel universe?