We still haven’t established whether some form of warp drive is doable or not. Even if you can’t move faster than light, if you can distort spacetime around yourself sufficiently in the right way, you can maybe get a functionally-similar effect.

https://en.wikipedia.org/wiki/Alcubierre_drive

The Alcubierre drive ([alkuˈβjere]) is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.[1][2] Proposed by theoretical physicist Miguel Alcubierre in 1994, the Alcubierre drive is based on a solution of Einstein’s field equations. Since those solutions are metric tensors, the Alcubierre drive is also referred to as Alcubierre metric.

Objects cannot accelerate to the speed of light within normal spacetime; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination more quickly than light would in normal space without breaking any physical laws.[3]

The local velocity relative to the deformed space-time would be subluminal, but the speed at which a spacecraft could move would be superluminal, thereby rendering possible interstellar flight, such as a visit to Proxima Centauri within a few days.