What assumptions underlie the proof that singularities are inevitable?

In summary, the conversation revolves around the topic of singularities in the context of Hawking's 1996 book and Penrose's references to it. The person speaking has ordered the book and is expecting it to help them understand the energy conditions that are assumed in the singularity theorems. They are also interested in studying Chapter 4 of the notes provided in order to gain a better understanding of the subject. The person also mentions a technical exposition written by an expert that they believe will provide valuable information.
  • #1
gnnmartin
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TL;DR 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.
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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  • #3
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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  • #5
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.
 

1. What is a singularity?

A singularity is a point in space and time where the laws of physics break down and traditional mathematical equations are no longer applicable.

2. What assumptions are made in the proof that singularities are inevitable?

The proof of the inevitability of singularities is based on several assumptions, including the validity of general relativity, the existence of black holes, and the assumption that matter and energy in the universe are evenly distributed.

3. How do these assumptions lead to the conclusion of inevitable singularities?

The assumptions mentioned above, along with other mathematical and physical principles, are used to create models of the universe that show how matter and energy behave under extreme conditions. These models consistently predict the formation of singularities, leading to the conclusion that they are inevitable.

4. Are there any alternative theories that challenge this proof?

Yes, there are alternative theories that challenge the inevitability of singularities. Some propose modifications to general relativity, while others suggest entirely new theories of gravity. However, these alternative theories have not been widely accepted or proven, and the proof of inevitable singularities remains the most widely accepted explanation.

5. What are the implications of the inevitability of singularities?

The inevitability of singularities has significant implications for our understanding of the universe and the laws of physics. It suggests that there are limits to our current knowledge and that there may be phenomena that we cannot fully explain or understand. It also has practical implications for space travel and the study of black holes.

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