What assumptions underlie the proof that singularities are inevitable?

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Discussion Overview

The discussion revolves around the assumptions underlying the proof that singularities are inevitable, particularly in the context of the singularity theorems developed by Penrose and Hawking. Participants explore the theoretical foundations, including energy conditions and their implications for the Einstein tensor.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant mentions that they have read about an energy condition that may restrict the Einstein tensor, seeking clarification on which specific energy condition applies and how it constrains the tensor's values.
  • Another participant points out that the discussion pertains to the singularity theorems devised by Penrose and Hawking, suggesting a specific chapter from lecture notes as a resource for further study.
  • A participant references Penrose's work, noting that he states singularities are inevitable under certain weak conditions related to causality and energy positivity in Einstein's theory, and expresses a desire to understand these assumptions better.
  • Links to technical resources, including a paper and a lecture, are shared to aid in understanding the topic.
  • One participant acknowledges the contributions of others and expresses hope that the provided references will yield the desired information.
  • Another participant briefly mentions energy conditions without elaboration.

Areas of Agreement / Disagreement

Participants appear to share an interest in understanding the assumptions related to singularity theorems, but there is no consensus on the specific energy conditions or their implications, indicating that multiple viewpoints and uncertainties remain.

Contextual Notes

The discussion highlights the need for clarity on the definitions and implications of energy conditions, as well as the specific assumptions that lead to the conclusion of inevitable singularities, which are not fully resolved in the conversation.

gnnmartin
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TL;DR
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
 
Last edited:
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.
 
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Energy conditions, for instance.
 

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