A What assumptions underlie the proof that singularities are inevitable?

AI Thread Summary
The discussion centers on the assumptions underlying the proof of the inevitability of singularities in the context of general relativity, particularly referencing the works of Penrose and Hawking. Key assumptions include energy conditions that impose restrictions on the Einstein tensor, which are crucial for the singularity theorems. The inquiry seeks clarity on which specific energy condition applies and how it constrains the Einstein tensor's values. Relevant resources, including Penrose's "The Road to Reality" and various academic papers, are suggested for further exploration of these concepts. Understanding these foundational assumptions is essential for grasping the implications of singularities in theoretical physics.
gnnmartin
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In ‘The Road to Reality’ Roger Penrose states (page 733, note 27.20 to text on page 713) that “singularities are inevitable (assuming certain very weak and reasonable conditions concerning causality and energy positivity in the Einstein theory)” I would like to know what these assumptions are.
Poking around on the internet has not helped me. Penrose references Hawking and his 1996 book and I have ordered that, but I suspect my progress through that book will be slow. I have read that the assumptions include an energy condition, which I assume is expressed as a restriction on the Einstein tensor, but would like to be sure, and to be sure which energy condition and how it constrains the value of the Einstein tensor.
 
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gnnmartin said:
Summary:: In ‘The Road to Reality’ Roger Penrose states (page 733, note 27.20 to text on page 713) that “singularities are inevitable (assuming certain very weak and reasonable conditions concerning causality and energy positivity in the Einstein theory)” I would like to know what these assumptions are.
A technical (but also somewhat pedagogical) exposition written by an expert:

https://arxiv.org/abs/2108.07296
 
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ergospherical, George Jones, matinbn, thanks to all of you for the references. I haven't yet looked at them, but I am hopeful that they will give me the information I want.
 
Energy conditions, for instance.
 
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