What assumptions underlie the proof that singularities are inevitable?

[gnnmartin]

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.

 

[ergospherical]

It concerns the singularity theorems devised by himself and Hawking. An entry point is to study Chapter 4 (beginning p.47) of the following notes: https://www.damtp.cam.ac.uk/user/hsr1000/black_holes_lectures_2020.pdf

 

[George Jones]

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

 

[martinbn]

This is the Hawking part of the book. Your question needs only the first lecture, the classical theory.
https://arxiv.org/abs/hep-th/9409195

 

[gnnmartin]

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.

 

[independentphysics]

Energy conditions, for instance.