Black hole vs mathematical singularity

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SUMMARY

The discussion clarifies the distinction between mathematical singularities and black hole singularities within the framework of General Relativity (GR). It asserts that mathematical singularities arise from the limitations of GR as a model, indicating that these infinities signal a breakdown in the theory rather than a physical reality. The consensus among physicists is that future theories of quantum gravity should ideally eliminate singularities, as infinities are not compatible with established numerical frameworks. The conversation highlights the ongoing challenges in reconciling quantum mechanics and cosmology with the concept of singularities.

PREREQUISITES
  • Understanding of General Relativity (GR)
  • Familiarity with mathematical singularities
  • Basic knowledge of quantum mechanics
  • Concepts of cosmology and physical modeling
NEXT STEPS
  • Research quantum gravity theories and their implications on singularities
  • Study the role of infinities in mathematical physics
  • Explore advanced topics in cosmology related to black holes
  • Investigate the limitations of General Relativity in extreme conditions
USEFUL FOR

Physicists, cosmologists, and students of theoretical physics seeking to understand the implications of singularities in the context of General Relativity and future quantum gravity theories.

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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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