The influence of Penrose's singularity theorem in General Relativity

TL;DR

This paper reviews the impact of Penrose's 1965 singularity theorem on General Relativity, discussing its developments, misconceptions, and modern perspectives on trapped surfaces, highlighting its foundational role in understanding gravitational fields.

Contribution

It provides a comprehensive overview of the theorem's influence, clarifies misconceptions, and introduces a modern perspective on trapped surfaces in gravitational theory.

Findings

Advancements inspired by Penrose's theorem over the years.

Clarification of common misconceptions about the theorem.

Proposal of a modern perspective on trapped submanifolds.

Abstract

Penrose's crucial contributions to General Relativity, symbolized by his 1965 singularity theorem, received (half of) the 2020 Nobel prize in Physics. A renewed interest in the ideas and implications behind that theorem, its later developments, and other Penrose's ideas improving our understanding of the gravitational field thereby emerged. In this paper I highlight some of the advancements motivated by the theorem that were developed over the years. I also identify some common misconceptions about the theorem's implications. A modern perspective on the concept of closed trapped submanifolds, based on the mean curvature vector, is advocated.