I am a mathematically minded individual. I do not intuitively comprehend physics, and as a sophomore in high school who has only taken Intro to Physics in his freshman year, I may very well have a completely erroneous view of many concepts within physics.
Recently, Einstein's model of gravity has been on my mind. I was watching the following lecture here wherein Professor Sera Cremonini explains that gravity is due to the curvature of 4 dimensional spacetime, and that this curvature is caused by the mass of objects within the universe. Furthermore, the higher the curvature (equivalently, the higher the mass of an object) the higher the force of gravity near that object. To illustrate this, she uses a stretched rubber disk and puts a large ball on it whilst smaller balls are on the disk. The large ball causes the rubber to stretch, and this curvature causes the smaller balls to be pulled toward the large ball just as gravity causes orbits of the solar system. This made me think.
Theoretically, is it possible for the curvature of the universe at one particular point to be so strong that the gravitational force is infinite? If infinite is ridiculous in this context, consider the question reformulated: Is there, or can there be, a point in the universe where the curvature is greater than any other point in the universe? If so, why doesn't the strength of gravity at this point cause the entire universe to be contracted to this point? That is, isn't this just like the Big Crunch?
Once again, I don't know if I've conveyed this using the proper terminology and I'm aware it's a very bizarre idea. I hope you all can entertain my thoughts and attempt to answer my question as best as possible, and correct my understanding and terminology as warranted.