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

Since the beginning of mankind, Homo sapiens have endeavoured to understand their relationship to the world as a structure of meanings. Where do we come from? How do we relate to the other living beings that inhabit the planet with us? How are we part of an infinite universe? Spiritual beliefs and myths, but also scientific observations and the resulting world views change over time and are an expression of how we humans interpret our relationship to the world.

We are increasingly exploring and penetrating the world. We decipher connections, we organise, quantify and name. We have created ever more complex instruments to do this. We find methods, formulate verifiable theorems and establish causalities between cause and effect. Researchers describe the world as it is, both physically and biologically. They use science to formulate terms and concepts and constantly achieve verifiable results. They decode the world and follow methodical procedures that open up immense possibilities for action. In this way, we make the world available to us. But science does not set itself the task of asking about the meaningfulness of life.

And what does art do? Art leads everything back to us. It asks about the meaning of knowledge for us. Artists are concerned with perception, or rather, with the nature of experience itself. How we perceive, visually, linguistically and aesthetically, but also how the experience of life takes place as an existential experience of “being in the world”. And art can transform our relationship with the world through narratives, through images and sounds, through poetry, into an experience of resonance.

Both science and art have their origins in intuition, imagination and conjecture. While scientists have to create evidence, artists can proceed more freely and make associations and imagination the material of their narratives. The meaning of existence and the experience of transcendence can hardly be found in science. We humans have to find them within ourselves. And we often create symbols to do so.

The Presence of Absence highlights matter as a presence into which life imprints itself. Energy and life are potent yet transient. The interplay between life, energy and matter is a central theme of the exhibition.

The exhibition will spatially juxtapose exhibits that translate the abstract concept of the “presence of absence” into an expanded realm of thought from both artistic and scientific perspectives. Works by significant contemporary artists will engage in dialogue with scientific exhibits from geology and astrophysics, including casts from Pompeii, footprints of prehistoric humans from the Laetoli site in present-day Tanzania and replicas of prehistoric cave paintings.

The curatorial narrative explores the astrophysical phenomenon of black holes. Concepts of expansion, time and the infinite cosmos challenge our understanding. Simultaneously, they provoke questions about our identity and origins. Our planet hovers somewhere between the boundless and the eternal. For a fleeting moment, the window of our lives opens, revealing the unique experience of our existence through our bodies, senses and minds. Each exhibit, in its own distinct way, engages with this existential exploration of being and humanity across the dimensions of space and time.

With this exhibition, we also trace the origins of art as a fundamental human desire to express abstract ideas. Why did Homo sapiens, tens of thousands of years ago, carve animal figures and abstract geometric shapes into the walls of deep caves? Why did they create images of things that were understood by others as symbols, serving as a connection to higher, non-manifest, spiritual realms? Why did Homo sapiens, unlike other species, develop a need for transcendence?

One of the countless stories and myths that moved us is recorded by Pliny the Elder in his Natural History, written around 77 years AD, shortly before he met his death in the fiery ash rain of Pompeii: the myth of Butades of Sicyon, the Corinthian potter, and his daughter. The story goes like this: the young girl loved a young man who had to leave for a long journey. As the separation approached, the girl drew the outline of her lover’s head against the wall where the light of the fire fell. The father, moved by her plight, filled in this shadow image with colour and made a clay imprint of the outline, which he then fired. According to Pliny’s myth, art arises from the desire to capture the transient and fleeting; to preserve it out of wistfulness and longing, absence and memory, but also out of love and through beauty. This parable is touching because it embodies such fundamental feelings.

The outline, the stone wall and the fire—doesn’t this remind you of the earliest cave paintings and engravings found by palaeoanthropologists and archaeologists on every continent? Were these the origin of art at the dawn of humanity?

The oldest evidence is attributed to the Blombos Cave in South Africa, dating back 140,000 years. With the migrations of Homo sapiens, cave art spread across every continent. Despite such incredibly extended time periods, this early art exhibits similar techniques and motifs. These seem to have been passed down from group to group, from generation to generation, long before the physiological evolution of the larynx and brain suggested the emergence of language and writing.

For tens of thousands of years, humans—early artists—created images of animals, human figures and abstract signs. Did they grapple with the same questions and ideas that modern humans do?

The cave paintings of the San people in South Africa and Botswana, or those from the Magdalenian culture of the Stone Age in Europe, served as a readable visual language for early humans. They depicted the experienced environment while also representing the spiritual cosmos of these ancient people. The stone walls, where humans created their paintings, far from the outside world and deep in the darkness of the earth, were more than just canvases. They were like a skin that separated this world from the other. Negative forms and imprints of human hands have been found in caves on every continent. These suggest the magic of contact, the touch of a hand on the surface of the rock as a gateway to another world. Leaving a handprint may have been part of a sacred act of connection with an invisible beyond—a transcendental experience. It is evidence of the primordial human need and eternal quest for a deeper relationship with a reality beyond the individual.

Awe in the face of nature. The feeling that there is more than we know. The striving to understand, to perceive through both our senses and our minds the eternal structures that reveal the order of everything in this universe and ourselves as part of it.

Since the dawn of humanity, people have gazed at the night sky. “Mathematics is the language in which the book of the universe is written”, said Galileo Galilei. It is a way of assigning meaning to symbols that can then be read and understood by others. Mathematics is a universal language of human thought, and mathematical rules reflect the order found in all natural processes, whether it’s the Fibonacci sequence or Einstein’s equations. This makes mathematics the purest form of expressing universal principles. Music follows precise mathematical structures, the growth of plants, the sequence of tides and every form of existence can be described by mathematical equations. Yet, there remains so much that humanity does not yet understand. Time and again, the power of the human mind will strive to push these boundaries.

What is the origin of all matter on earth and in the infinity of the cosmos? What effects do natural events create that reshape the earth and affect people’s lives with their power? And how do people deal with the existential need to face eternity in their finiteness? What myths and images do they create in order to connect with the spiritual? Is art a way of immortalising oneself in time? The exhibition is dedicated to these questions, which have been driving the human imagination from prehistoric times to the present day. Ever since we humans have existed on earth, we have created stories, symbols and signs to give form to our feelings, thoughts and knowledge, to leave traces in time and perhaps to connect with eternity.

We experience the miracle of reality through the senses of our body. This consists of the elements of exploding stars in space: the nitrogen in our DNA, the calcium in our bones, the iron in our blood and the carbon in our cells. In fleeting moments, we connect with eternity and give traces of existence a material form. Art is one way of doing this.

I would like to thank Claudio Parmiggiani, Indigo and Mayo Bucher, the sons of Heidi Bucher, Toni R. Toivonen, Petra Noordkamp, the artists of the Marshmallow Laser Feast collective and Lawrence Malstaf, as well as the institutional lenders, Dr Gabriel Zuchtriegel and the Archaeological Park of Pompeii, Prof Dr Fabio Martini and Dr Lapo Baglioni of the Florentine Museum and Institute of Prehistory “Paolo Graziosi”, the Natural History Museum Vienna, the LWL-Museum of Natural History in Münster, Nicolò Stabile, founder of the initiative Il Cretto è casa mia of the survivors of the earthquake in the town of Gibellina, as well as the photographer Giuseppe Ippolito, the VR creator Alberto Stabile and the writer Giovanna Giordano. I would like to thank the Italian Consulate General for its patronage. I would especially like to thank Prof Dr Andreas Mulch, Director of the Senckenberg Research Institute and Natural History Museum Frankfurt, and Prof Dr Luciano Rezzolla from the Institute for Theoretical Physics at the Goethe University Frankfurt for a time of joint thinking and working.

Franziska Nori
Director Frankfurter Kunstverein