English

Light Rays, Singularities, and All That

High Energy Physics - Theory 2023-07-14 v6 General Relativity and Quantum Cosmology

Abstract

This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics that was held at the IAS as well as the New Zealand Mathematical Research Institute summer school held in Nelson in January, 2020.

Cite

@article{arxiv.1901.03928,
  title  = {Light Rays, Singularities, and All That},
  author = {Edward Witten},
  journal= {arXiv preprint arXiv:1901.03928},
  year   = {2023}
}

Comments

104 pp. V2: Various corrections/improvements, especially in Appendix C. New Appendix D added, V3: minor corrections and improvements to figures., V4: minor corrections and another new Appendix, V5,V6: minor corrections

R2 v1 2026-06-23T07:09:55.691Z