How far could a spaceship go if we never ran out of thrust? (2020)

Re:How far could a spaceship go if we never ran out of thrus... by cout on Tuesday August 10, 2021 @07:48AM (#28127644)

I understand how there can be no center if the universe has positive curvature. But if the universe is saddle-shaped and non-infinite, surely there has to be a center?

[ Parent | on HN ]

Re:How far could a spaceship go if we never ran out of thrus... by effie on Tuesday August 10, 2021 @10:03AM (#28129000)

I think not; consider pseudosphere, there is no obvious center. Its embedding in 3D space has infinite dimensions but the object itself has finite surface area.

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

If you mean object with finite dimensions and negative curvature and no center, there seems to be such a thing, see Fig. n066200e:

https://encyclopediaofmath.org/wiki/Negative_curvature,_surf...

EDIT

Rozendorn's idea seems to be still an open question:

https://mathoverflow.net/questions/52851/the-geometry-of-nad...

[ Parent | on HN ]

Re:How far could a spaceship go if we never ran out of thrus... by feoren on Tuesday August 10, 2021 @04:18PM (#28133811)

Rather than think "surface of a balloon inflating", think "surface of an (infinite?) rubber sheet being uniformly stretched". It does intuitively seem like if there is 0 curvature and no "center", then the universe must be infinite though ...

[ Parent | on HN ]