Abstract:
Black holes are the most enigmatic objects in the Universe, their secrets forever veiled from the outside. Yet an elusive idea, conceived by Roger Penrose while crossing the street, opened an unexpected window onto their inner nature. Outlined in just a couple of pages over six decades ago, this insight would ultimately be recognized with the 2020 Nobel Prize in Physics.
This colloquium explores Penrose’s pioneering singularity theorem—the first of what would later become known as the singularity theorems—and its enduring significance. After a brief journey through the historical context, we will uncover the essential ideas behind the theorem using only basic notions of geometry, introducing the mathematical concept of curvature and its deep connection to gravity. We will then examine its physical implications and lasting impact, illustrated with simple but revealing examples.