Curved space

I am trying to imagine how space curves as a planet passes through. I
have seen the graph like grids curving away from the object/planet,
but nothing in 3D.

Is space rigid enough that it creates a "bow wave and wake?" If so how
far away from the local passage does the wave go? Does it extend into
space indefinitely setting up interference patterns as the curve
passes other curves?

Or, is space compressible like jello? Is the curve only local due to
space viscousness?

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