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Since black holes make an infinitly deep gravitational well, is it okay to say that it isn't a "well" to some extent, but instead a "hole" in the spacetime fabric?
Answer 1:

Given our current established theories, yes. At the center of a black hole, we have the singularity and that basically punctures a hole in space time. However, most physicists suspect that nothing in our universe is really ever infinite, and so newer theories are being created to try and solve this problem. String theory is probably the most well known and most developed (in its various forms) but there are a few other alternatives as well.


Answer 2:

It's a "singularity" - a point where the curvature of space-time reaches an undefined, infinite level. The effect is similar to what happens when you divide something by zero.


Answer 3:

It's a well with a hole at the bottom. Near--but not inside--the black hole, there is still a gravitational well.



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