Prof Dr Luciano Rezzolla, Institute for Theoretical Physics, Goethe University Frankfurt

“Physics is all about using the transcendence of mathematics to reveal the immanence of the Universe we live in. Taking a photo of a black hole is a perfect example of how an object whose existence was purely mathematical, has been transformed into a physical object by the collaborative work of hundreds of scientists. The exhibition guides the visitor into this journey from Mathematics to Physics, from Absence to Presence, and back”.

Prof Dr Luciano Rezzolla, Institute for Theoretical Physics at Goethe University Frankfurt

 

Beauty and Complexity

Einstein’s Field Equations of General Relativity and Schwarzschild Solution of the Black Hole, 1915
ADM Equation by Arnowitt, Misner and Deser
CCZ4 Equation by Alic, Bona-Casas, Bona, Palenzuela, Rezzolla
Foil print on plexiglass, each 150 x 85 cm
Courtesy Prof Dr Luciano Rezzolla, Institute for Theoretical Physics, Goethe University Frankfurt

Often in modern physics a theory swings between the presence of beauty but the absence of complexity, and the absence of beauty but the presence of complexity. This happens every time the theory goes from being formulated in its idealised form – when the mathematical beauty prevails and the complexity is hidden – to being expressed under realistic conditions as those needed for actual calculations – when then the mathematical beauty fades away to be replaced by a less beautiful complexity.

The first line on the left panel reports the Einstein equations that fully describe the theory that revolutionised of our understanding of gravity. The second line shows instead the solution found by the Frankfurter Karl Schwarzschild and representing a black hole. In both cases, simple beauty hides the enormous complexity of Einstein’s theory or the challenges behind the concept of a black hole.

The middle panel reports the Einstein equations when written in a form that is commonly used to represent physical laws. In this case, the four-dimensional spacetime (that is, the combination of space and time) is split into a three-dimensional space and a one-dimensional time. A transition between beauty and complexity starts to emerge.

The right panel reports the same Einstein equations written on the left when expressed in the form that is needed to solve these equations with the help of supercomputers. Written in this way, Einstein equations can be used to calculate, for instance, what happens when two neutron stars collide and produce a black hole. In this case, complexity (that nevertheless has a beauty of its own…) replaces the compact beauty of the Einstein equations.

 

Seeing what cannot be seen

The Black Hole Sagittarius A*, 2022
Digital print on black Forex, 150 x 150 cm
© Event Horizon Telescope collaboration et al.
Courtesy Prof Dr Luciano Rezzolla, Institute for Theoretical Physics, Goethe University Frankfurt

In April 2017, scientists of the international collaboration “Event Horizon Telescope” (EHT) used eight high-frequency radio telescopes scattered around the globe to collect radio waves emitted from the very centre of our galaxy.

In April 2022, after three years of meticulous analysis of the data and on its theoretical modelling, the EHT presented to the world the image of Sagittarius A*, the black hole at the centre of the Milky Way, and that is presented here.

What is colloquially defined as a “photo” is in reality a map of the intensity of the radio emission averaged over time. What is peculiar about this image – that looks like a doughnut – is the approximately circular form of the bright part and the presence of a dark region of at the centre, a region that scientists call the “shadow” of the black hole.

The shadow, which is a precise prediction of Einstein’s theory of General Relativity, reveals the presence of an event horizon and hence of a black hole. Mathematically, a black hole is a solution in vacuum of the Einstein equations in vacuum, that is, in the absence of any form of matter or energy. Yet, the presence of the black hole is manifested via the spacetime curvature it produces and that changes the motion of objects near it.

Because the event horizon absorbs the light produced in its vicinity, the centre of the photo is darker as it “steals” light we would otherwise receive. At the same time, near the event horizon, where temperatures are high and the emission enhanced, light can still be emitted without being absorbed by the black hole. This is the light we effectively receive and is shown in the photo.

 

Touching what cannot be touched

Black Hole SgrA* as a tactile 3D model, 2024
⌀ 19,5 cm, height 6 cm
Produced for the exhibition The Presence of Absence with support from the European Research Council (ERC)
Courtesy Prof Dr Luciano Rezzolla, Institute for Theoretical Physics, Goethe University Frankfurt

The event horizon, that is, the outer surface of a black hole, cannot be seen because light cannot be emitted from this surface, where gravity is extreme.

Yet, the presence of a black hole can be deduced in terms of its “shadow”, that is, the dark depression at the centre of the large image on the wall produced by the International Collaboration “Event Horizon Telescope” (EHT). The dark region reflects the absence of light near the event horizon and has allowed us to “see” a black hole at the centre of the Galaxy (Sgr A*) as predicted by Einstein’s theory of General Relativity.

What if we cannot see? How can a black hole be “seen” by those of us whose eyes cannot receive light?

What is shown is a 3D rendering of the intensity of the radio emission from Sgr A* and you are welcome to explore it with your hands. In this way, you can imagine how a blind person can perceive it. The rendering also helps our minds imagine the very strong curvature of space and time that develops near a black hole and that is well reproduced by the steep walls of the print near the centre of the shadow.

 

Revealing the Presence

Glass hologram cube of photon trajectories curved by the gravitational pull of a black hole, 2024
15 x 15 x 15 cm, Glass
Produced for the exhibition The Presence of Absence at Frankfurter Kunstverein with support from the European Research Council (ERC)
Courtesy Prof Dr Luciano Rezzolla, Institute for Theoretical Physics, Goethe University Frankfurt

A black hole is a solution of the Einstein equations in the absence of matter, that is, in vacuum. Its outer edge is represented by the “event horizon”, a geometrical surface where gravity is so strong that nothing, not even light, can leave it. Hence, it is possible to enter the event horizon but not to leave it.

Because it cannot emit light, the event horizon of a black hole cannot be “seen”, at least in terms of light rays. However, the motion in its vicinity of light rays can reveal its presence.

The block shows the trajectories of light rays, or photons as physicists also call them, as they approach or leave a rotating black hole. The complex and sometimes bizarre trajectories they follow are the result of the strongly warped spacetime. The cube helps understand that the two-dimensional image of a black hole we measure with radio telescopes and the resulting photo is really the product of the three-dimensional motion of light rays coming from all directions and being deflected by the black hole.

These trajectories provide information not only on the presence of a black hole but also on its properties, that is, the mass and spin (how rapidly it rotates). Shown on one of the sides of the cube is an almost circular shape that scientists call the “shadow” of the black hole. Measuring the size and shape of the shadow helps them reveal the presence of a black hole and understand its properties.

Texts by Prof. Dr. Luciano Rezzolla