## Light travel in space of varying timeflow

I'm having trouble to visualise this scenario. Please help to sort it out. Just an exercise to perceive relative timeflows.

Suppose perfectly flat empty space. Suppose there are regions of space where timeflow slows down twice. Suppose a rocket at c/2 travelling through such region of space. Now there are 2 perceptions of that space region, one for external observer, and other for travelling observer.

For external observer, rocket approach that space, slows down to c/4 (same distance in twice external time), take some time to pass it, then accelerate back to c/2 again.
For observer on rocket, no slowdown, instead that section of space seems to be passed faster (timeflow change is not perceived) than expected when calculated outside, or perceived acceleration occurs.

Velocity=distance/time. We measure distances in ct.

If velocity of light c is fixed, then in regions of space where timeflow changes, it must be perceived as variation of distance. Or, while entering such space region, visual perception of stars or external objects should change as if they jump off further away, and then back closer when leaving that region. But, because there was perceived acceleration through that space, this cancels out in forward direction, and perceived is uniform travel velocity through that region. Only visual perception changes due to limited c.

For external observer, light travelling through that region seems to take unexpectedly more external time than would be calculated outside based on flat space. Or, basically, for external observer that region of space seems 'larger' than expected from flat space, or is 'curved'.

If the region of space is spherical with uniform spread of time rate around it, would it look like gravitational spacetime curvature?

I'm confused about perceived time and space dilation for observers. Is it at all reasonable path of thinking?