[whatshisface]

>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.

[otikik]

I thought wether or not a singularity sits at the center of a black hole is actively discussed.

Or to be more precise: our math seems to indicate that there is one ... and precisely because of that we think that our math might be wrong or incomplete (because every single time we have encountered an "infinite" or something resembling that in the past it turned to be an error).

[colechristensen]

General Relativity says there is a singularity, more than one depending on the metric and coordinate system chosen.

However GR is not a quantum theory and it is well known that it clashes with quantum mechanics in ways that would show up in a singularity so what the physical reality of space actually at and nearby the singularity is still a mystery because we don't yet have an accepted theory of quantum gravity.

[lisper]

[deleted because brain wedgie]

[colechristensen]

That's literally the rest of my comment.

[lisper]

Sorry about that.

[lotw_dot_site]

>they're space-time shapes with a singularity at the middle

Upon googling "black hole singularity", the first "People also ask" is "Does black hole contain singularity" and the answer is, "No, black holes in our universe, that is to say the real universe, do not contain singularities." While this doesn't in itself invalidate your point, it does seem to raise questions.

>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.

I think what you are doing here is conflating the physical effects of the thing (the gravitational field of force) with the mathematical description of the thing itself (a precisely defined geometric structure). If you are talking about extremely strong gravity fields, such as those that bind entire galaxies (or galaxy clusters or even larger organizational patterns), then that is one class of things (empirical), but the purely theoretical notion of physical singularities is an entirely different class of things altogether (a class, which, IMO is perfectly self-contradictory).

>That's because solutions to the Laplace equation smooth themselves out as quickly as possible as you move away from the boundary condition.

This seems incorrect. I find that solutions to the Laplace equation typically "smooth themselves out" in a quasi-linear way (ie, the way sines and cosines do). The most vexing question in Quantum Mechanics is in fact why quantum states (i.e. the eigenfunctions that are solutions to PDE's such as Laplace's equation) appear to us as localized packets rather than how their "wave functional" mathematical descriptions would dictate (diffuse). The way this conundrum is resolved in QM is by way of a perfectly ad-hoc procedure called "collapsing the wave function".