If I understand the answers provided in this Link Why singularity in a black hole, and not just "very dense"? Then the singularity at $r=0$ may just be a mathematical artifact, and may not actually be physically realistic. If so then what's the fuss about within the scientific community about black holes being singularity points as if it applies in the real physical world, why don't we treat theoretical singularity points and realistic black holes separately why must we associate real black holes with the mathematical artifacts we call singularities?
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$\begingroup$ Related post by OP: physics.stackexchange.com/q/817720/2451 $\endgroup$– Qmechanic ♦Commented Jun 9 at 5:24
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$\begingroup$ Yes they are related but not the same, you provided this link physics.stackexchange.com/q/18981/2451 which I referred to in this current question in response to physics.stackexchange.com/q/817720/2451 and after going through the question and it's answer... this question came up in my mind as well and now I ask. $\endgroup$– Precious AdegbiteCommented Jun 9 at 6:13
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$\begingroup$ Your question is meaningless, as it assumes a lot of things to be true that are not. To name a few: (1) “GR predicts singularities” - false. The existence of the inner singular spacetime is an assumption with no rigorous proof. (2) You say: “black holes being singularity points” - A Schwarzschild singularity is an infinitely long line. (3) You say: “singularity at $r=0$” - Here $r$ is not the radial distance. The actual radius of the horizon measured in meters is zero. (4) You say: “singularity […] in the real physical world” - It cannot be created for as long as the universe exists. $\endgroup$– safesphereCommented Jun 11 at 4:31
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$\begingroup$ (5) “what's the fuss about within the scientific community” - Or is it rather in the popular press? (6) “why don't we treat theoretical singularity points and realistic black holes separately” - Everyone with the proper understanding does. (7) “mathematical artifacts” - Here you imply that that there is something wrong with singularity where GR breaks. This is false. GR does not break at the singularity. GR predicts that geodesics end there and so they do. There is no contradiction or paradox whatsoever. (8) “very dense” - A Schwarzschild singularity is moment of time, not an object. $\endgroup$– safesphereCommented Jun 11 at 4:58
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2 Answers
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Why don't we treat theoretical singularity points and realistic black holes separately?
Because black holes, as we understand them presently, are the prediction of GR, and the same theory results in singularity near their center. So unless and until we can come up with a theoretical framework that agrees with the prediction of GR and at the same time have singularity-free black holes, we would have to settle with the GR definition of black holes.
Singularity-free black holes are called regular black holes in the literature, and work on them is ongoing, e.g., see this review.
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$\begingroup$ Wow thanks, your reference to regular singularity-free blackholes... should really be helpful, at least that's a realistic way to describe blackholes, I should really follow it up. Although someone once suggested this in one of my past questions now it comes up again interestingly. $\endgroup$ Commented Jun 9 at 6:28
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Why must we associate real black holes with the mathematical artifacts we call singularities ?
The simplest model of the interior (inside the event horizon) of a black hole that is consistent with GR leads to a singularity at the point $r=0$. This singularity is generally believed to be not physically possible, in which case the simple GR model of the interior of a black hole must be incorrect.
I don't think there is a "fuss" about this, but it does naturally lead physicists to want to know how to build a better model of the interior of a black hole (and especially the region near $r=0$). There are various alternatives, including non-singular black hole models, fuzzballs (the string theory solution) and Planck stars (the loop quantum gravity solution). Without a generally accepted theory of quantum gravity, we don't have a good way to choose between these alternatives.
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$\begingroup$ Understood, thank you very much!😉 $\endgroup$ Commented Jun 9 at 15:25