The 1965 Penrose singularity theorem - by Josť M M Senovilla and David Garfinkle 2015 - Article review

This document contains article review "The 1965 Penrose singularity theorem" by Josť M M Senovilla and David Garfinkle written in 2015
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1. Introduction.

Penrose's theorem is, without a doubt, the first such theorem in its modern form containing new important ingredients and fruitful ideas that immediately led to many new developments in theoretical relativity, and to devastating physical consequences concerning the origin of the Universe and the collapse of massive stars, see sections 5 and 6.
I doubt if any form of mathematics can physical explain the origin of the Universe or the collapse of massive stars. First always comes a physical description of what is involved and there after (if possible) a mathematical description.
The fundamental, germinal and very fruitful notion of closed trapped surface is a key central idea in the physics of Black Holes, Numerical Relativity, Mathematical Relativity, Cosmology and Gravity Analogues.
Also here I have certain doubts.

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2. Before 1955

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2.3 The Oppenheimer-Snyder model

This turned out to be of enormous relevance for the study of compact stars, since in 1931 Chandrasekhar unexpectedly found an upper mass limit for white dwarf stars in equilibrium, even when taking into account the quantum effects
The reference of the mass of a white dwarf star is a physical important fact.
This implied that stars with a larger mass will inevitably collapse.
Even more important. See also Reference #53
Then, the question of massive neutron cores (or stars) was addressed in [242] by using a cold Fermi gas equation of state and GR.
They found another mass limit for equilibrium and concluded that, even allowing for deviations from the Fermi equation of state, a massive enough neutron star will contract indefinitely never reaching equilibrium again.
Again this seems a contradiction between mathematics and physics (physical observations). If that is the case the mathematics should be modified.
They proved using general arguments that, in spherical symmetry, values of r = alpha would eventually be reached, that light emitted from the star would be more and more redshifted for external observers - who would only see the star approach r --> alpha asymptotically -, and that the entire process will last a finite amount of time for observers comoving with the stellar matter.
It should be mentioned that what is discussed is physics and that evolution of these processes itself are completely indepent of any human activity. At the same time accurate observation of these processes can be twarted by using light, which behaviour can be influenced by these processes.
Hence, (i) the "Schwarzschild surface" r = alpha was indeed crossable by innocuous models containing realistic matter such as dust; and (ii) a careful analysis of the model shows that the star will end up in a catastrophic singularity where a(t) --> 0 and therefore space "vanishes" again.
It is not so much that space vanishes, but that matter disappears. This also demonstrates that there is something wrong with the mathematics used.
What did Einstein think about the singularities and all the previous results?
Both his thoughts should de handled separately.
Well, it is hard to tell, obviously, but it seems that he |and the orthodoxy| simply dismissed the known singularities as either a mathematical artifact due to the spherical symmetry, or as unattainable effects beyond the feasibility of the physical world.

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In summary, even though infinite values of physical observables must not be accepted in physical reality, one must be prepared to probe the limits of any particular theory, but this was reluctantly done in GR before 1955 despite many important indications that this was needed.
The infinite values are due to the mathematics used in the equations, which are descriptions of the physical reality. When the solutions are in conflict with the physical reality (observations) the equations should be modified.

3. From 1955 to 1965

4. The 1965 theorem, its implications and relevance

4. The 1965 theorem, its implications and relevance

5. After 1965: immediate impact of the theorem

6. Observational consequences: cosmic censorship, critical phenomena, BKL conjecture, etc.

7. Long-term impact of the theorem

8. XXI century singularity theorems

9. Concluding remark

Reflection 1 -

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Created: 10 Oktober 2020

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