Imagine your bed made up with a blanket on it.
That is a good example of flat space time.
Now let’s say you are in the middle, under the blanket because it is cold. That would be curved space time and you would be acting as the mass pulling the sheet closer to you.
Both of these are in reference to special relativity.
If you are asking about topology of Space-Time it gets a lot more complicated. Depending on the shape we can infere information that we might not be able to see from where we are.
For reading about the latter, look up Space-Time topogy and particle horizon.
Bonus fact: past the event horizon every path you can take leads into the center of the black hole (singularity).
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