re: Temporal discontinuity
I think temporal separations characterize the universe at various stages and locales. Life itself may experience temporal discontinuity, not spatial separation, but simply a difference in the pace at which we live.
If in 5 billion years we have become machines, or cyborgs, or something far beyond that even, then we may be more worried about surviving hardware failures expected to occur every 5 milliseconds (an eternity). We may do things so fast that a supernova would be a sluggish event, easily avoided, in fact the Sun itself might seem as frozen as the rest of the universe does today.