When I saw this on Twitter I mentally noted several predictions. And when I read the article, all of them turned out to be right...
1) This "time machine" spacetime will be closely related to the "warp drive" spacetimes described by Miguel Alcubierre.
2) The time machine solution to Einstein's field equations relies on the existence of material with negative mass. This is often described as "exotic matter" - which might sound like stuff we could build if only we were clever enough, like graphene, superconductors or plasmas. But negative mass is more akin to a square circle – words we can say, but something whose actual existence is fundamentally at odds with the way the universe works.
3) The authors of the the paper, Benjamin Tippett and David Tsang, have a great (and nerdy) sense of humour. It turns out that they also wrote a non-technical account of their work, entitled The Blue Box White Paper.
4) So far as I can see, Tippett and Tsang aim to shed light on the deep structure of general relativity and have a little fun in the process. (Actually, that may be the other way round.) The paper is published in a reputable journal, Classical and Quantum Gravity and an earlier version is online for free at the ArXiV.
5) Tippett and Tsang are not trying to build a time machine. If you are trying to build a time machine, don't bother: even if we can design them, the universe makes it impossible for us (or anyone) to build them. But, like spacewarps, that won't stop people from trying.
6) This paper will not lead to a time machine, but it will inspire an awful lot of bad science journalism. And, hopefully, a few good teachable moments.
CODA: As all time-travel fans will know, the new Doctor Who series began screening this month. For some reason, a time-travelling police box seems perfectly reasonable... but a university academic with an office like the Doctor's? We can dream.