Mathematics, computer science and …black holes?

Markus Pössel

By now, the Lindau Lecture at the Heidelberg Laureate Forum is a treasured tradition: each HLF is joined by a Nobel Laureate talking about his or her work, and in turn, one of the mathematics or computer science laureates gives a lecture at each Lindau Nobel Laureate Meeting. But it’s rare for the connection with the HLF’s key topics of computer science and mathematics to mesh as tightly with a Nobel laureate talk than they did with this year’s talk by Reinhard Genzel, of the Max Planck Institute for Extraterrestrial Physics in Garching, who received the 2020 Nobel Prize in Physics (together with Andrea Ghez and Roger Penrose) for his work on the detection and characterisation of the black hole in the center of our very own Milky Way galaxy.

Using mathematics to hunt for black  holes – since 1784

The link with mathematics goes back a few hundred years: to Isaac Newton, who, had those two institutions existed back then, would surely have received both a physics Nobel Prize and a Fields Medal. After all, he invented in parallel a theory of mechanics and gravitational interaction, and the necessary formalism in the shape of the differential and integral calculus – which happens to be the basis of much of today’s mathematics. Genzel began the historical background portion of his talk with the two scientists who used Newton’s formalism to first derive something analogous to a black hole: a body so compact that its (Newtonian) escape velocity is greater than the speed of light; no light can escape from the surface of such a body to infinity.

One of them was Pierre-Simon Laplace, who is one of the mathematicians that brought Newton’s theory into the modern form we learn today. The other was John Michell, who in a 1784 article described the plan for what Genzel and his colleagues would achieve roughly 200 years later. Regarding the sort-of-black-holes he has just described, which are by definition themselves not visible, Michell speculates that “if other luminous bodies should happen to revolve about them we might still perhaps from the motions of these revolving bodies infer the existence of the central ones with some degree of probability” – which, of course, is just what Genzel’s group – and independently Andrea Ghez’s – did: they tracked the motion of stars around our Milky Way’s central black hole, and from the stellar motion deduced the black hole’s presence as well as the black hole’s mass.

Journey with hard- and software

But the journey (here illustrated with a video from ESO, the European Southern Observatory, whose telescopes the Genzel group used) takes us from mathematics to computer science, as well.

The actual observations, as Genzel made clear, would not have been possible without cutting-edge hardware and software: control systems in the “adaptive optics” system that deform a mirror so as to counteract the image distortions due to turbulence in the Earth’s atmosphere, as well as camera chips sensitive to infrared radiation for the observations themselves. Last but not least, the computing power to put everything together: reconstruct the stellar motions around the black hole, and from there deduce the black hole’s mass. Genzel’s reply to the question by a participant about how computer scientists can help with this kind of research boiled down to the statement that astronomers have always been among the first customers for whatever new and powerful computers are available – from data analysis to comprehensive simulations of the history of the universe as a whole. When it comes to black holes, Lindau and Heidelberg can be much closer than you might think.

The post Mathematics, computer science and …black holes? originally appeared on the HLFF SciLogs blog.