# Light Rays, Singularities, and All That

## TL;DR

This paper introduces key causal concepts in General Relativity, discussing singularity theorems, black hole properties, and topological censorship, based on lectures from 2018 and 2020.

## Contribution

It provides an accessible overview of fundamental causal theorems and their implications in General Relativity, synthesizing recent lecture material.

## Key findings

- Explanation of the Raychaudhuri equation
- Summary of Penrose and Hawking singularity theorems
- Discussion of the Gao-Wald theorem

## 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.