In 3D visualizations, why does spacetime curve toward, not away from objects?

Question

In all the ones I've seen, it appears to curve toward the object, which appears to be inconsistent with 2D visualizations.

Answer 1

By 2D visualizations, I presume you mean this:

• As you can see in the picture, spacetime is bending down toward the object, Earth. This way, if there is an object near Earth, they will travel toward each other, similar to two objects on a stretched blanket. In contrast, if spacetime bent up and away from the objects, they would be pushed apart. See this video for a visualization. You may find it interesting.
• The reason for why spacetime curves toward objects and not away is because if it curved "away", the objects would be pushed apart. In the 2D model, spacetime curves toward the object. In a 3D model, spacetime also curves toward the object.

There is far more to this answer if you look into Einstein's Theory of General Relativity, but my knowledge of physics is not adequate enough to explain it all in one answer. I hope this helped!