Physical Relevance of Singularity Theorems?

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Discussion Overview

The discussion revolves around the relevance of singularity theorems in the context of modern cosmological models, particularly in light of the existence of a positive cosmological constant. Participants explore the implications of these theorems for understanding singularities in the universe, including their applicability to black holes and the early universe.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant references a review paper by Senovilla & Garfinkle, suggesting that the positive cosmological constant may render much of the theory surrounding singularity theorems irrelevant to real-world scenarios.
  • Another participant counters that the relevance of singularity theorems might depend on the success of proposed "no singularity" solutions, which could violate key assumptions of the theorems, particularly energy conditions.
  • A different viewpoint suggests that singularity theorems contribute to framing the general problem of singularities, potentially leading to new variations of existing theorems that could address different conditions.
  • One participant expresses skepticism about the optimistic interpretations of the implications of singularity theorems.

Areas of Agreement / Disagreement

Participants express differing views on the relevance and implications of singularity theorems, with no consensus reached on their applicability to real-world scenarios or the validity of proposed solutions.

Contextual Notes

The discussion highlights the dependence on specific assumptions and conditions in singularity theorems, as well as the unresolved nature of how these theorems relate to current cosmological models.

strangerep
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I've been reading this recent review paper by Senovilla & Garfinkle on The 1965 Penrose singularity theorem.

In sect 8.3 (p38):
Senovilla & Garfinkle said:
[...] the existence of a positive cosmological constant ##\Lambda>0##, which is just the wrong sign for the curvature condition (6) used in the focusing effect and, ultimately, in most singularity theorems.
Their eqn(6) is on p8: ##R_{\rho\nu} u^\rho u^\nu ~\ge~ 0 ~.##

The message I take away from this is that much of the theory about singularity theorems has turned out to be irrelevant to the real world.

Or am I missing something? :oldconfused:
 
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strangerep said:
The message I take away from this is that much of the theory about singularity theorems has turned out to be irrelevant to the real world.

I would say might turn out to be irrelevant to the real world. It depends on how the various proposed "no singularity" solutions for the early universe and for black holes (actually "apparent" black holes if the proposals work out, since the proposed solutions contain no event horizons, only apparent horizons) pan out. If they work out, then yes, it would be true that the singularity theorems only apply to solutions that turn out not to describe the real world--in the solutions that describe the real world, key assumptions that go into the singularity theorems are violated (mainly the energy conditions).
 
One could argue that an additional contribution of the singularity theorems is that it they frame how to think about the general problem of singularities ( not tied to a particular class of solutions ). If more cases are needed, then they may arise as variations of existing theorems... possibly with different ways of imposing conditions needed to complete the proofs.
 
Hmm. Wishful thinking? :rolleyes:

(Anyway, thanks for the comments. :oldbiggrin: )
 

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