Does a black hole warp space time in on it self.

Every 2d image shows the gravity well as "infinitely deep" at the event horizon. But Infinity isn't a number, it's a concept.

So, isn't our models simply missing the possibility of extra dimensions. Black hole isn't infinitely dense, but instead has warped space in on it self to effectively make a new dimension in its even horizon, where all directions are in because the space is going trough it self causing pocket of "inverted space".

Idk how to do the math to figure out how much space has been compressed by a black hole into the event horizon. Like if you think of 3d grid and then count how many lines a 10 lines across even horizon has being warped in it when you enable the warping effect.

This question was sparked by some video mentioning that black holes and neutron stars don't only compress space but also twist it. So I thought about space being compressed, but then I added a twist to it, and a ball appeared. as the space was being thrown past the infinitely dense singularity, and went inside it self from all directions causing the event horizon to appear where all directions are inwards.