Question How to understand how large celestial objects interact with space-time fabric?

[guimondb]

How do planets and other celestial bodies affect space-time fabric. For large and dense objects such as the sun and black holes, how can we visualize how these objects affect space-time. As seen in this image:

https://imgur.com/0EWQk9j

View: https://imgur.com/0EWQk9j
, it seems that these large objects in space "sink" down into space due to their density. If this indeed is the case wouldn't space as a whole need to be flat for this visualization of objects affecting space-time to be correct. If however, space isn't flat and this visualization still holds true, what dictates the direction that the objects sink in and would it be possible to travel to the underside of the divot created by said object:

https://imgur.com/PeQH0fO

View: https://imgur.com/PeQH0fO
.

 

[akashrao]

i simply understand that space-time fabric is an idea generated under the impact of mass of a body and its gravitational pull ... where there is more mass per less volume the space-time fabric shrinks or gets curved or gets more of itself in there ... where there is rarity the space-time fabric is regular and normal ...

 

[Catastrophe]

I think your difficulty is two-fold.
1. You are thinking in a lower dimension. Like you could think of a black hole as existing in spherical space and pulling towards the centre.
2. Arising from (1) you are thinking of gravity as downwards from the horizontal whereas, if the bh is not existing in a flat medium, the direction is perpendicular to the surface at that point.

Perhaps someone more knowledgeable than I can correct this, but I think this is a problem in visualisation.