Black hole vs mathematical singularity

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The discussion highlights the distinction between mathematical singularities and black hole singularities, emphasizing that the singularities in General Relativity (GR) are mathematical constructs. Physicists generally view these singularities as limitations of current theories, suggesting that GR may not accurately describe reality at those extremes. There is hope that future theories of quantum gravity will eliminate singularities, as infinities are problematic in physics. Infinities often arise from inadequate modeling, and their resolution is anticipated to improve understanding in quantum mechanics and cosmology. Ultimately, addressing these infinities is crucial for advancing theoretical physics.
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What is the difference between mathematical singularity and black hole singularity[emoji780]
 
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GR is a theory expressed in terms of maths. The singularities it produces are mathematical singularities.

That said, most physicists believe that the singularities are really just the mathematics throwing up its hands and saying "I dunno". That is, we believe that somewhere between the regimes we have tested and the singularity GR stops being an accurate model of reality. And we hope that a future theory of (quantum?) gravity won't include singularities.
 
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Infinities do not play well with other numbers. In no small part because infinity in NOT a number. In most theories infinities that pop up in the math vanish when proper physical modeling is applied. In quantum mechanics and cosmology some still persist - probably because of reliance upon dubious approximations applied to their modeling. The resolution of these infinities will be a welcome relief to physicists, who have lost their limited sense of humor at being face smacked by them.
 
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Thread 'Matter density right after the decoupling'

https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
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