Alexey Bobrick and Gianni Martire propose a warp-bubble drive. It's Alcubierre without the silly. It's Lentz but better explained.
The ship still takes a generation (from our perspective) to get anywhere good, like Gliese 876. But time slows down inside the bubble, so it's not a Generation Ship mess like Kim Robinson's Aurora or that Aniara poem. And it doesn't need dangerously relativistic speed like Tau Zero. The travellers' relatives on Earth still have to wait it out. The travellers won't.
This will be nice to have closer home for interplanetary transfers as well. Although, as Lentz, the spacetime-bending physics here look to require some hardcore energy in-system.
FOLLOWUP 1/16/22: Sabine says that Jessica Santiago rules out everybody except Bobrick-Martire. Lentz, last we looked, won't give up yet. I didn't pay attention to the Santiago paper because, drrrp, causality; intuitively any FTL is bollocks. As for Martire, whose warp escapes Santiago; Sabine relays that he is hiring.
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