It is with greatest joy that we welcome the awarding of the Nobel Prize to Roger Penrose, Reinhard Genzel, and Andrea Ghez. At the heart of this prize lies one of the most mysterious and fascinating predictions of Einstein's general relativity: black holes. These are regions of spacetime which you can enter but then only to vanish forever from the visible part of our universe. Black holes are surrounded by an event horizon which acts as a one-way membrane: you can cross it only from the outside to the inside. Shortly after Einstein created his theory, Schwarzschild discovered the first and simplest black hole on paper, without realising what it really was.

It took many physicists and years to understand the black hole nature of the Schwarzschild solution, and it took Roger Penrose to invent a mathematical theory which shed light on the geometry of black holes. His “Lorentzian causality theory” was the key to describe and locate event horizons, and to analyse their properties. He used his beautiful theory to settle a controversy which existed at the time, whether singularities - regions where spacetime stops - are an accident of the Schwarzschild solution or a general property of black hole universes. His conclusion was: singularities are an inseparable feature of black holes.

All this was recognized, quite justly, by the Swedish Academy of Science, as groundbreaking for the amazing observations by Reinhard Genzel, Andrea Ghez, and their teams, of Sagittarius A^* - the “dark heart of our galaxy”. Many years of observations, with unprecedented resolution, allowed them to measure accurately the orbits of dozens of stars moving around the center of our galaxy. This in turn led to the calculation of the mass of the object sitting there, which is about four million solar masses. Such massive objects are not unusual in the universe, but they tend to emit a lot of light, which is not the case in the center of our galaxy: it is much darker than expected for such a mass. The only coherent model, within our current theories, of a dark object with such a mass is that of a black hole. Our galaxy is far from special in this respect, and these observations, together with many others, make us believe that most galaxies have a supermassive black hole at their center.

Sir Roger Penrose's influence on contemporary theoretical physics goes well beyond his studies of black holes. Along with Yvonne Choquet-Bruhat, from the French Academy of Sciences, he is the father of mathematical general relativity. His “cosmic censorship hypothesis”, stating that spacetimes singularities are clothed behind event horizons, has been at the center of research of mathematical general relativity for decades, and will continue far into the future.

His “Weyl curvature hypothesis” provides an elegant approach to the nature of the big bang singularity. The conjectured “Penrose inequality”, tying the mass of black holes with their areas, has inspired some of the most interesting mathematical papers in geometry in recent years. His invention of "twistors", a new kind of geometric objects, has led to a new branch in geometry, with unexpected recent applications in quantum field theory. Amongst his striking inventions are the “Penrose tilings”: this is the perverse idea that there exist tiles which can be used to cover a surface in a pattern without any translational symmetries. His suggestions about the role of gravity in quantum physics might well turn out to be a stepping stone for the grail of contemporary physics: a theory of quantum gravity.

We are happy to report that Roger Penrose has been a frequent visitor to Vienna. He gave public lectures at our Faculty, the ESI and the ISTA with overflowing audiences. His treatise with the Viennese-born Wolfgang Rindler on spinors is a classic.

His most recent paper, on the interaction of gravity with quantum physics, was written in collaboration with Yvette Fuentes, professor in our Faculty from 2015 until 2018. Current and past members of the Vienna relativity group made significant contributions to the questions raised by Roger Penrose, including a monograph on strong cosmic censorship, studies of twistors, spinors, and of the conformal structure of spacetime (one more topic initiated by Penrose), proofs of special cases of the Penrose inequality, and extensions of his Lorentzian causality theory to spacetimes with pathological properties. A recent Master Thesis in our group revisits his flagship “singularity theorem”, while a book I have just published in Oxford University Press applies Penrose's tools to study the “Geometry of Black Holes”.