Well, time does very concretely swap roles with one of the spatial dimensions, namely the radial one. They change signs in the metric, making the radial dimension timelike and the old temporal dimension spacelike.
Re:The Nobel Prize in Physics 2020
by SiempreViernes on Tuesday October 06, 2020 @07:17AM
(#24696561)
I think there is more to the special status of time than just the sign convention used, so I find this mathematical detail about as interesting as the singularity on the event horizon.
In practice it just means that wherever you try to go you'll end up in the same place, basically you're going down a funnel and the exceptional thing is that the funnel is made out of spacetime itself.