Physical Relevance of Singularity Theorems?

In summary, the conversation discusses the relevance of singularity theorems, specifically the Penrose singularity theorem, in the real world. It is noted that the existence of a positive cosmological constant, which goes against the curvature condition used in the theorem, may render the theorem irrelevant. However, it is also mentioned that the theorem provides a framework for thinking about singularities and could potentially be adapted to other cases.
  • #1
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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  • #2
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).
 
  • #3
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.
 
  • #4
Hmm. Wishful thinking? :rolleyes:

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

1. What is the physical significance of singularity theorems?

Singularity theorems are important in understanding the nature of black holes and the limits of our current understanding of physics. They provide mathematical proof that under certain conditions, a singularity (a point of infinite density and curvature) must exist within a black hole. This has significant implications for our understanding of general relativity and the behavior of matter in extreme conditions.

2. How do singularity theorems relate to the Big Bang theory?

Singularity theorems also have implications for the beginning of the universe. According to the Big Bang theory, the universe began as a singularity that expanded rapidly. Singularity theorems provide mathematical evidence for the existence of this singularity and help us understand the physics behind the early stages of the universe.

3. Can singularity theorems be tested or observed in real life?

Singularity theorems are based on mathematical models and cannot be directly tested or observed in real life. However, their predictions and implications can be tested through observations of black holes and the behavior of matter in extreme conditions.

4. Are there any exceptions to singularity theorems?

While singularity theorems are based on rigorous mathematical proofs, there are some exceptions and limitations. For example, quantum effects may play a role in preventing the formation of a singularity, and the singularity itself may not be a true point of infinite density, but rather a region of extreme curvature.

5. How do singularity theorems impact our understanding of the universe?

Singularity theorems challenge our current understanding of the laws of physics and the behavior of matter in extreme conditions. They also provide insight into the origins and evolution of the universe, and can potentially lead to new theories and advancements in our understanding of the universe.

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