>a person is referring to some object that has the shape of a mathematical point
Black holes aren't points, they're space-time shapes with a singularity at the middle and a spherical event horizon. The black hole at the center of our galaxy extends across 16 million miles, or a little over eighteen times the size of our sun.
If the singularity at the middle is slightly modified to be something else according to a better theory of gravity (most physicists believe that this will eventually happen), the outlying spacetime will not change very much, for reasons similar to how Newton was able to work out how the planets moved around the sun without knowing what the sun was made of or what was inside it.
If you imagine a circus tent propped up in the middle by a square pole, it will look very much like one propped up by a round pole. That's because solutions to the Laplace equation smooth themselves out as quickly as possible as you move away from the boundary condition.
Black holes aren't points, they're space-time shapes with a singularity at the middle and a spherical event horizon. The black hole at the center of our galaxy extends across 16 million miles, or a little over eighteen times the size of our sun.
If the singularity at the middle is slightly modified to be something else according to a better theory of gravity (most physicists believe that this will eventually happen), the outlying spacetime will not change very much, for reasons similar to how Newton was able to work out how the planets moved around the sun without knowing what the sun was made of or what was inside it.
If you imagine a circus tent propped up in the middle by a square pole, it will look very much like one propped up by a round pole. That's because solutions to the Laplace equation smooth themselves out as quickly as possible as you move away from the boundary condition.