Visualizing Curved Space-Time in 2D

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kevin_13
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General Relativity explains that every single piece of mass alters the space-time fabric, creating a curve. But since we live on a three-dimensional universe shouldn't the curvature alter the fabric in every dimension, creating some kind of weird closed curve that might look as a bubble around the mass.
I really cannot visualize the curvature working in 2D.
I don't know if you understand what I mean, if not sorry I'm not very good at physics
(excuse my ignorance).
 
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Here is some material that might help you to understand curvature in two spatial dimensions, which is the simplest kind to understand: http://www.lightandmatter.com/html_books/genrel/ch05/ch05.html#Section5.3

The curvature described by general relativity isn't 2-dimensional or 3-dimensional, it's four-dimensional, because time is included as a dimension.
 
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