Here you find an online version of the annex with all notes and references as printed in the book.

Prologue – And We Really Can See Them

  1. Live stream of the EU press conference in Brussels: ESO press release: Video zooming in on the black hole: NSF press conference:
  2. See photo insert, Figure 1, page 1.

Chapter 1 – Humankind, the Earth, and the Moon

  1. The air density in low Earth orbit is 5 x 10–9 g/cm3, as opposed to a normal air density of 1,204 kg/m3 (10–3g/cm3): Kh. I. Khalil and S. W. Samwel, “Effect of Air Drag Force on Low Earth Orbit Satellites During Maximum and Minimum Solar Activity,” Space Research Journal 9 (2016): 1–9,
  2. Ethan Siegel, “The Hubble Space Telescope Is Falling,” Starts with a Bang, Forbes, October 18, 2017, /the-hubble-space-telescope-is-falling/#71ac8b1b7f04; Mike Wall, “How Will the Hubble Space Telescope Die?”, April 24, 2015, .com/29206-how-will-hubble-space-telescope-die.html.
  3. Job 26:7 (King James Version).
  4. Psalms 90:4 (KJV).
  5. S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, “27Al+ Quantum-Logic Clock with a Systematic Uncertainty below 10–18,” Physical Review Letters 123 (2019): 033201,
  6. Rømer and Huygens used the orbit of the moon Io around Jupiter as a clock and determined that this clock ran a bit slow when the Earth was farther away from Jupiter in its orbit around the sun than a few months before. The light from Jupiter arrives a few minutes later than expected; the Io clock lags behind.
  7. Michelson was born in Prussia and moved to the United States with his parents at age two:
  8. It’s not certain, however, that Einstein was influenced by the Michelson-Morley experiment in a crucial way. The near relativity of electromagnetism was probably more important. See Jeroen van Dongen, “On the Role of the Michelson-Morley Experiment: Einstein in Chicago,” Archive for History of Exact Sciences 63 (2009): 655–63,
  9. “Andre and Marit’s Moon bounce wedding,” YouTube, February 15, 2014,
  10. Adam Hadhazy, “Fact or Fiction: The Days (and Nights) Are Getting Longer,” Scientific American, June 14, 2010,
  11. M. P. van Haarlem, and 200 contributors, “LOFAR: The Low Frequency Array,” Astronomy and Astrophysics 556 (2013): A2.

Chapter 2 – The Solar System and Our Evolving Model of the Universe

  1. P. K. Wang and G. L. Siscoe, “Ancient Chinese Observations of Physical Phenomena Attending Solar Eclipses,” Solar Physics 66 (1980): 187–93,; also see
  2. Yuta Notsu, et al., “Do Kepler Superflare Stars Really Include Slowly Rotating Sun-like Stars?: Results Using APO 3.5 m Telescope Spectroscopic Observations and Gaia-DR2 Data,” The Astrophysical Journal 876 (2019): 58, https://ui.adsabs…876…58N.
  3. Tweet by Mark McCaughrean, @markmccaughrean, January 5, 2020,
  4. Knowledge of many Stone Age artifacts (the Lascaux cave, carvings on an eagle bone in the Dordogne, Stonehenge, the lunar map at Knowth) remains vague and contested. See Karenleigh A. Overmann, “The Role of Materiality in Numerical Cognition,” Quaternary International 405 (2016): 42–51,; P. J. Stooke, “Neolithic Lunar Maps at Knowth and Baltinglass, Ireland,” Journal for the History of Astronomy 25, no. 1 (1994): 39–55, Nevertheless, human curiosity argues against assumptions that humans only began studying the sky with the advent of verifiable written sources.
  5. Jörg Römer, “Als den Menschen das Mondfieber packte,” Der Spiegel, July 16, 2019,
  6. The International Celestial Reference System (ICRS) is a system of coordinates that is compiled from Very Long Baseline Interferometry (VLBI) observations of quasars; the orientation of the Earth in space within this system is determined according to International Earth Rotation and Reference Systems Services (IERS) Earth Orientation Parameters. It can be used, for example, to connect coordinates on Earth in the International Terrestrial Reference System (ITRS) with satellite coordinates:
  7. John Steele, A Brief Introduction to Astronomy in the Middle East (London: Saqi, 2008). Scholars of the ancient Middle East have encountered evidence of ersatz kings. In Mesopotamia, at the time of a solar or lunar eclipse, a puppet ruler was placed on the throne in place of the king who had been marked by an evil omen. A prisoner or mentally challenged person was chosen for the purpose. During this time the real king lived as a simple peasant. Only after a hundred days had passed did the priests give the all clear.
  8. Matthew 2:1–13 (KJV). Nowhere in the biblical text is it actually stated that they are kings, or that there are three of them. Usage and historical context make it probable that the figures referred to here are astrologically trained experts. More details can be found in my WordPress blog post on the subject (Heino Falcke, “The Star of Bethlehem: A Mystery (Almost) Resolved?” October 28, 2014, and in the literature cited in the post, in particular, George H. van Kooten and Peter Barthel, eds., The Star of Bethlehem and the Magi: Interdisciplinary Perspectives from Experts on the Ancient Near East, the Greco-Roman World, and Modern Astronomy (The Hague: Brill Academic Publishers, 2015).
  9. Bede, De Natura Rerum; Johannes de Sacro Bosco (b. 1230 AD), Tractatus de Sphaera, see
  10. John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (New York: Overlook Press, 2014).
  11. Sebastian Follmer, “Woher haben die Wochentage ihre Namen,” Online Focus, September 11, 2018, -ihre-namen-alle-details_96962.
  12. The astronomy of the Indian astronomer Aryabhata (b.476AD) was geocentric but posited that the Earth rotated; see Kim Plofker, Mathematics in India (Princeton: Princeton University Press, 2009). For more on Indian astronomy, see N. Podbregar, “Jantar Mantar: Bauten für den Himmel,”, September 15, 2017,
  13. Joseph Needham, with the research assistance of Wang Ling, Science and Civilisation in China: Vol. 2, History of Scientific Thought (Cambridge: Cambridge University Press, 1956), cited in “The Chinese Cosmos: Basic Concepts,” Asia for Educators,
  14. For example, see Peter Harrison, The Territories of Science and Religion (Chicago: University of Chicago Press, 2015). A summary written by the author can be found here:
  15. Another such myth, also well-known from film, is the murder of Hypatia by a Christian mob and the burning down of the Library of Alexandria. It doesn’t diminish Hypatia’s significance as a courageous, wise woman to note that her case doesn’t serve to support the “science versus Christianity” thesis. The murder was more political in nature—the library didn’t really exist anymore as such— and besides all that, there is scant factual evidence. See Charlotte Booth, Hypatia: Mathematician, Philosopher, Myth (Stroud, UK: Fonthill, 2016). See also Maria Dzielska, “Hypatia wird zum Opfer des Christentums stilisiert,” Der Spiegel, April 25, 2010,; and further, Cynthia Haven, “The Library of Alexandria—Destroyed by an Angry Mob with Torches? Not Very Likely,” The Book Haven (blog), March 2016,
  16. Hans Lipperhey from Middelburg is generally regarded as the inventor of the telescope, but there are others who claimed this invention as their own.
  17. Mario Livio, Galileo and the Science Deniers (New York, Simon & Schuster, 2020). For a contrasting view, see this review of the book: Thony Christie, “How to Create Your Own Galileo,” The Renaissance Mathmeticus (blog), May 27, 2020, Christie shows that much of our present-day image of Galileo has been poeticized, and pulls no punches in his criticism of Livio’s book.
  18. Ulinka Rublack, Der Astronom und die Hexe: Johannes Kepler und seine Zeit (Stuttgart: Klett-Cotta, 2019).
  19. Newton was a professor of theology and was known among his peers as an outstanding Bible scholar, though he also explored alchemical and heretical ideas in secret. Robert Iliffe, “Newton’s Religious Life and Work,” The Newton Project,
  20. In Episode IV, Han Solo proudly declares that he once made the Kessel run in 12 parsecs. This sounds like a description of time, but in the opinion of some fans is meant to be an indication of distance. See Astronomers always shift uncomfortably in their seats whenever they hear this line.
  21. Alberto Sanna, Mark J. Reid, Thomas M. Dame, Karl M. Menten, and Andreas Brunthaler, “Mapping Spiral Structure on the Far Side of the Milky Way,” Science 358 (2017): 227–30,…358..227S.

Chapter 3 – Einstein’s Happiest Thought

  1. This might be more of a philosophical question, but a completely empty space has zero entropy and does not develop; thus, there’s no time to measure either. A completely empty space without matter or vacuum energy would be nothingness in the truest sense of the word, and physics has nothing to say about it—though mathematics might.
  2. Light is used here in a more general sense and includes all forms of interactions that are mostly conducted at the speed of light. Space has no meaning in a hypothetical universe with matter that never interacts. Here the question presents itself as to what we should call reality. The solutions to Einstein’s field equations exist just as well without there having to be any light or matter in space-time. Of course, then space and time are reduced to a purely mathematical concept described by the term nothingness.
  3. For example, Philip Ball, “Why the Many-Worlds Interpretation Has Many Problems,” Quanta Magazine, October 18, 2018,; Robbert Dijkgraaf, “There Are No Laws of Physics. There’s Only the Landscape,” Quanta Magazine, June 4, 2018, https://www.quanta
  4. The process by which quantum states experience loss of information on their way to becoming macroscopic objects is generally described by the concept of decoherence. A more thorough, broadly accessible treatment of quantum physics can be found, for example, in Claus Kiefer, Der Quantenkosmos: Von der zeitlosen Welt zum expandierenden Universum (Frankfurt: S. Fischer, 2008).
  5. There are historical reasons for the fact that physicists speak in terms of the speed of light. From a modern point of view it would also be possible to name this absolute maximum speed the “speed of gravity,” after gravitational waves, or better yet the “speed of causality.” In the theory of relativity, the speed of light is a fundamental quality of space-time, namely the natural relationship of the spatial scale to the timescale.
  6. J. C. Hafele and Richard E. Keating, “Around-the-World Atomic Clocks: Predicted Relativistic Time Gains,” Science 177 (1972): 166–68, https://ui.adsabs.harvard .edu/abs/1972Sci…177..166H. What’s important is that all three clocks are moving—relative to a nonrotational “inertial system,” like the center of the Earth or the fixed stars! At the equator, a clock on the ground moves east at about 1,600 km/h. If we fly east in an Airbus A330 traveling 900 km/h, then our velocity is the velocity of the plane plus the Earth’s rotation, up to 2,500 km/h. Flying west, we move 900 km/h slower relative to the center of the Earth than the Earth’s surface—so just about 700 km/h, but ultimately still traveling east! The Mr. Clock that flew east was traveling fastest relative to the center of the Earth and thus time passed most slowly for it, relatively speaking. The Mr. Clock that flew west moved slowest, relatively speaking, and so time passed most quickly. The clock that waited dutifully on the ground also wasn’t standing still relative to the center of the Earth. It provides us with a reference time and ticked slower than a clock at the center would have, faster than the clock flying east, and slower than the clock flying west. Thus, the experiment indeed tests aspects of the general theory of relativity and the equivalence principle.
  7. R. Malhotra, Matthew Holman, and Thomas Ito, “Chaos and Stability of the Solar System,” Proceedings of the National Academy of Science 98, no. 22 (2001): 12342–43,…9812342M.
  8. My colleague Paul Groot was our department head for many years.
  9. The physicist and mathematician Pierre-Simon Laplace was responsible for an important step forward in the development of celestial mechanics with his 1823 work Traité de mécanique céleste. The mathematician Urbain Le Verrier succeeded in predicting Neptune’s existence by studying disruptions in Uranus’s orbit in 1846.
  10. Einstein started as a third-tier employee, but he’d been promoted by the time he published the theory.
  11. Hanoch Gutfreund and Jürgen Renn, The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity” (Princeton: Princeton University Press, 2015).
  12. Pauline Gagnon, “The Forgotten Life of Einstein’s First Wife,” Scientific American, December 19, 2016, A somewhat different portrayal is offered in Allen Esterson and David C. Cassidy, contribution by Ruth Lewin Sime, Einstein’s Wife: The Real Story of Mileva Einstein-Maric (Boston: MIT Press, 2019).
  13. The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity” (Princeton: Princeton University Press, 2015), 57.
  14. Albert Einstein, “How I Created the Theory of Relativity,” reprinted in: Y. A. Ono, Physics Today 35, no. 8 (1982): 45,
  15. Strictly speaking, the equivalence principle only applies to a point mass, since in this example Einstein’s feet would be pulled down to Earth with a tiny bit more force than his head. This is a result of what are called tidal forces. Earth is comparatively small, so the effect is minimal. While falling into a small black hole, however, Einstein would definitely notice something; in fact he’d be spaghetti-fied.
  16. Anicetestoftheequivalenceprinciplehasbeenperformedwithradio- astronomical measurements of a pulsar in a triple-star system with two white dwarfs:
  17. Hanoch Gutfreund and Jurgen Renn, The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity” (Princeton: Princeton University Press, 2015).
  18. Daniel Kennefick, “Testing Relativity from the 1919 Eclipse: A Question of Bias,” Physics Today 62, no 3. (2009): 37,
  19. The light is deflected half by the curvature of space and half by the curvature of time. The latter is already accounted for in Newton’s theory, which therefore predicts half the value of the deflection.
  20. J.-F. Pascual-Sánchez, “Introducing Relativity in Global Navigation Satellite Systems,” Annalen der Physik 16 (2007): 258–73,…519..258P. By a simple calculation, an error of 39 microseconds per day equals a positioning error of about 10 kilometers. This is stated in many popular articles, but it’s not clear whether this applies to the actual system, where all the satellite clocks are making a comparable error. More precise calculations are in the works (M. Pössel and T. Müller, in progress).
  21. A good overview of general relativistic effects as they relate to GPS can be found in this article: Neil Ashby, “Relativity in the Global Positioning System,” Living Reviews in Relativity 6 (2003): article no. 1,
  22. With thanks to Jun Ye for this tip. E. Oelker, et al., “Optical Clock Intercomparison with 6 x 10–19 Precision in One Hour,” arXiv eprints (February 2019),

Chapter 4 – The Milky Way and Its Stars

  1. See Spectroscopy in the glossary.
  2. Joshua Sokol, “Stellar Disks Reveal How Planets Get Made,” Quanta Magazine, May 21, 2018,
  3. A small number of the hydrogen atoms in us were probably never in stars, but rather have been drifting through space in diffuse gas since the Big Bang.
  4. Originally, the planet Dimidium was called “51 Pegasi b.” This is also the name that most astronomers would recognize.
  5. J. E. Enriquez, et al., “The Breakthrough Listen Initiative and the Future of the Search for Intelligent Life,” American Astronomical Society Meeting Abstracts 229 (2017): 116.04,…22911604E.

Chapter 5 – Dead Stars and Black Holes

  1. G. W. Collins, W. P. Claspy, and J. C. Martin, “A Reinterpretation of Historical References to the Supernova of AD 1054,” Publications of the Astronomical Society of the Pacific 111, no. 761 (1999): 871–80,
  2. Some researchers do link the Chaco Canyon pictograph with the supernova of 1054, which appeared on July 4, 1054, in the eastern part of the constellation Taurus: Doubt has recently been cast on this interpretation, however: Clara Moskowitz, “‘Supernova’ Cave Art Myth Debunked,” Scientific American, January 16, 2014,
  3. Ingrid H. Stairs, “Testing General Relativity with Pulsar Timing,” Living Reviews in Relativity 6 (2003): 5, https//…..6….5S.
  4. M. Kramer and I. H. Stairs, “The Double Pulsar,” Annual Review of Astronomy and Astrophysics 46 (2008): 541–72,
  5. Andreas Brunthaler found the supernova SN 2008iz by chance in his data.
  6. N. Kimani, et al., “Radio Evolution of Supernova SN 2008iz in M 82,” Astronomy and Astrophysics 593 (2016): A18,…593A..18K.
  7. J. R. Oppenheimer and G. M. Volkoff, “On Massive Neutron Cores,” Physical Review 55, no. 374 (1939): 374—but neutron stars were first proposed by Baade and Zwicky: W. Baade and F. Zwicky, “Remarks on Super-Novae and Cosmic Rays,” Physical Review 46 (1934): 76–77,…46…76B.
  8. Schwarzschild probably didn’t find the solution in Russia, but rather on the western front in the southern Vosges, as a letter to Arnold Sommerfeld makes clear:
  9. A few months later the Dutch scientist Johannes Droste independently found an even more elegant solution—which was roundly ignored, because Droste had only published it in Dutch. At this time it was still important to be able to communicate in German.
  10. Hanoch Gutfreund and Jurgen Renn, The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity” (Princeton: Princeton University Press, 2015).
  11. “LEXIKON DER ASTRONOMIE: Schwarzschild-Lösung,”
  12. As I was writing I thought I’d come up with something really original in using a river analogy to describe a black hole, but apparently somebody’s already written a whole academic article about it: Andrew J. S. Hamilton and Jason P. Lisle, “The River Model of Black Holes,” American Journal of Physics 76 (2008): 519–32, An entire collection of visual models depicting the general theory of relativity can be found here: Markus Pössel, “Relatively Complicated? Using Models to Teach General Relativity at Different Levels,” arXiv eprints (December 2018): 1812.11589,
  13. Jeremy Bernstein, “Albert Einstein und die Schwarzen Löcher,” Spektrum der Wissenschaft, August 1, 1996,
  14. Here a point does not mean a point in space in the sense found in the general theory of relativity. The central singularity is a boundary of infinitely curved space-time.
  15. Ann Ewing, “‘Black Holes’ in Space,” The Science News-Letter 85, no. 3 (January 18, 1964): 39,
  16. Roy P. Kerr, “Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics,” Physical Review Letters 11 (1963): 237–38,
  17. This effect is a significant factor in the formation of plasma jets around black holes, though not absolutely necessary. It is known under the term Blandford-Znajek process and is a variant of the Penrose process, in which rotational energy can be extracted from the black hole with the help of light or particles.
  18. Information about the Africa millimeter-wave telescope here:; M. Backes , et al., “The Africa Millimetre Telescope,” Proceedings of the 4th Annual Conference on High Energy Astrophysics in Southern Africa (HEASA 2016): 29,
  19. “Mistkäfer orientieren sich an der Milchstraße,” Spiegel Online, January 24, 2013,
  20. Dirk Lorenzen,“Die Beobachtung der Andromeda-Galaxie,”Deutschlandfunk, October 5, 2018,
  21. Trimble, V., “The 1920 Shapley-Curtis Discussion: Background, Issues, and Aftermath.” Publications of the Astronomical Society of the Pacific 107, no. 718 (1995): 1133,
  22. E. P. Hubble, The Realm of the Nebulae (New Haven: Yale University Press, 1936). Available online at:…..H.
  23. M. J. Reid and A. Brunthaler, “The Proper Motion of Sagittarius A*. III. The Case for a Supermassive Black Hole,” The Astrophysical Journal 892 (2020): 39,…616..872R.

Chapter 6 – Galaxies, Quasars, and the Big Bang

  1. Emilio Elizalde, “Reasons in Favor of a Hubble-Lemaître-Slipher’s (HLS) Law,” Symmetry 11 (2019): 15,…11…35E.
  2. Richard Porcas was the last person to photograph the 90-meter telescope in Green Bank. The photo has long hung in the hallway of the MPIfR in Bonn.
  3. Ken Kellermann, “The Road to Quasars” (lecture, Caltech Symposium: “50 Years of Quasars,” September 9, 2013),
  4. Maarten Schmidt, “The Discovery of Quasars” (lecture, Caltech Symposium: “50 Years of Quasars,” September 9, 2013),

Chapter 7 – The Galactic Center

  1. Charles H. Townes and Reinhard Genzel, “Das Zentrum der Galaxis,” Spektrum der Wissenschaft, June 1990,
  2. Pronounced “Sadge A Star.”
  3. When too much material falls toward a black hole, so much radiation is produced that the gas is blown away by the radiation pressure. The maximum limit of mass accretion is called the Eddington limit.
  4. Heino Falcke and Peter L. Biermann, “The Jet-Disk Symbiosis. I. Radio to X-ray Emission Models for Quasars,” Astronomy and Astrophysics 293 (1995): 665–82,…293..665F.
  5. Heino Falcke and Peter L. Biermann, “The Jet/Disk Symbiosis. III. What the Radio Cores in GRS 1915+105, NGC 4258, M 81, and SGR A* Tell Us About Accreting Black Holes,” Astronomy and Astrophysics 342 (1999): 49–56,…342…49F.
  6. Roland Gredel, ed., The Galactic Center, 4th ESO/CTIO Workshop, ASPC 102 (1996),
  7. A. Eckart and R. Genzel, “Observations of Stellar Proper Motions Near the Galactic Centre,” Nature 383 (1996): 415–17,
  8. B. L. Klein, A. M. Ghez, M. Morris, and E. E. Becklin, “2.2μm Keck Images of the Galaxy’s Central Stellar Cluster at 0.05 Resolution,” The Galactic Center 102 (1996): 228,
  9. A. M. Ghez, M. Morris, E. E. Becklin, A. Tanner, and T. Kremenek, “The Accelerations of Stars Orbiting the Milky Way’s Central Black Hole,” Nature 407 (2000): 349–51,
  10. Karl M. Schwarzschild, Mark J. Reid, Andreas Eckart, and Reinhard Genzel, “The Position of Sagittarius A*: Accurate Alignment of the Radio and Infrared Reference Frames at the Galactic Center,” The Astrophysical Journal 475 (1997): L111–14,…475L.111M.
  11. M. J. Reid and A. Brunthaler, “The Proper Motion of Sagittarius A*. II. The Mass of Sagittarius A*,” The Astrophysical Journal 616 (2004): 872–84,…616..872R.
  12. R. Schödel, et al., “A Star in a 15.2-Year Orbit Around the Supermassive Black Hole at the Centre of the Milky Way,” Nature 419 (2002): 694–96,
  13. L. Meyer, et al., “The Shortest-Known-Period Star Orbiting Our Galaxy’s Supermassive Black Hole,” Science 338 (2012): 84,…338…84M.
  14. R. Genzel, et al., “Near-Infrared Flares from Accreting Gas Around the Supermassive Black Hole at the Galactic Centre,” Nature 425 (2003): 934–37,
  15. F. K. Baganoff, et al., “Rapid X-Ray Flaring from the Direction of the Supermassive Black Hole at the Galactic Centre,” Nature 413 (2001): 45–48,…45B.
  16. Gravity Collaboration and R. Abuter, et al., “Detection of Orbital Motions Near the Last Stable Circular Orbit of the Massive Black Hole Sgr A*,” Astronomy and Astrophysics 618 (2018): L10,…618L..10G.
  17. Geoffrey C. Bower, Melvyn C. H. Wright, Heino Falcke, and Donald C. Backer, “Interferometric Detection of Linear Polarization from Sagittarius A* at 230 GHz,” The Astrophysical Journal 588 (2003): 331–37,…588..331B.
  18. H. Falcke, E. Körding, and S. Markoff, “A Scheme to Unify Low-Power Accreting Black Holes: Jet-Dominated Accretion Flows and the Radio/X-Ray Correlation,” Astronomy and Astrophysics 414 (2004): 895–903,…414..895F.
  19. F. Yuan, S. Markoff, and H. Falcke, “A Jet-ADAF Model for Sgr A*,” Astronomy and Astrophysics 383 (2002): 854–63,…383..854Y.

Chapter 8 – The Idea Behind the Image

  1. John 20:29 (KJV).
  2. The image resolution of a telescope is expressed in angular units, here in radians (rad): 2π rad equals 360o. The formula expresses, in terms of their angle to the line of sight, how far apart two points of light have to be in order to be distinguishable.
  3. Alan E. E. Rogers, et al., “Small-Scale Structure and Position of Sagittarius A* from VLBI at 3 Millimeter Wavelength,” Astrophysical Journal Letters 434 (1994): L59,…434L.59R.
  4. T. P. Krichbaum, et al., “VLBI Observations of the Galactic Center Source SGR A* at 86 GHz and 215 GHz,” Astronomy and Astrophysics 335 (1998): L106–10,…335L.106K.
  5. Heino Falcke, et al., “The Simultaneous Spectrum of Sagittarius A* from 20 Centimeters to 1 Millimeter and the Nature of the Millimeter Excess,” The Astrophysical Journal 499 (1998): 731–34,…499..731F.
  6. H. Falcke, et al., “The Central Parsecs of the Galaxy: Galactic Center Workshop” (proceedings of a meeting held in Tucson, Arizona, September 7–11, 1998),…..F.
  7. J. A. Zensus and H. Falcke, “Can VLBI Constrain the Size and Structure of SGR A*?,” The Central Parsecs of the Galaxy, ASP Conference Series 186 (1999): 118,
  8. A nice visualization of the paths the light takes can be found here: T. Müller and M. Pössel, “Ray tracing eines Schwarzen Lochs und dessen Schatten,” Haus der Astronomie,
  9. Tilman Sauer and Ulrich Majer, eds., David Hilbert’s Lectures on the Foundations of Physics 1915–1927 (Springer Verlag, 2009). See also: M. von Laue, Die Relativitätstheorie (Friedrich Vieweg & Sohn, 1921), 226.
  10. C. T. Cunningham and J. M. Bardeen, “The Optical Appearance of a Star Orbiting an Extreme Kerr Black Hole,” The Astrophysical Journal 183 (1973): 237–64,…183..237C; J.-P. Luminet, “Image of a Spherical Black Hole with Thin Accretion Disk,” Astronomy and Astrophysics 75 (1979): 228–35,….75..228L; S. U. Viergutz, “Image Generation in Kerr Geometry. I. Analytical Investigations on the Stationary Emitter-Observer Problem,” Astronomy and Astrophysics 272 (1993),…272..355V. For the first article the calculations and drawings were done by hand, for the second the calculations were done on the computer and the drawings done by hand, and for the third both calculations and drawings were done on the computer.
  11. Later, Professor Ferdinand Schmidt-Kaler, who at that time was trying to support my work and to whom I’m grateful for recommending me for the Akademiepreis of the Berlin-Brandenburg Academy of Sciences, informed me that a former student of his, just a few weeks after us and completely independent of us, had also entered the term shadow of a black hole into the literature—albeit in a very abstract and mathematical paper. A. de Vries, “The Apparent Shape of a Rotating Charged Black Hole, Closed Photon Orbits, and the Bifurcation Set A4,” Classical and Quantum Gravity 17 (2000): 123–44,
  12. Heino Falcke, Fulvio Melia, and Eric Agol, “Viewing the Shadow of the Black Hole at the Galactic Center,” The Astrophysical Journal 528 (2000): L13–16,…528L..13F.
  13. Heino Falcke, Fulvio Melia, and Eric Agol, “The Shadow of the Black Hole at the Galactic Center,” American Institute of Physics Conference Series 522 (2000): 317–20,
  14. Press release, “First Image of a Black Hole’s ‘Shadow’ May Be Possible Soon,” Max Planck Institute for Radio Astronomy in Bonn, January 17, 2000,

Chapter 9 – Building a Global Telescope

  1. The Max Planck Institute in Bonn and the Steward Observatory had built the Heinrich-Hertz Telescope (HHT), a 10-meter dish, on Mount Graham in Arizona together. When the Germans pulled out a few years later, it was renamed the Submillimeter Telescope (SMT) and the University of Arizona was working with great initiative to try to keep it alive on their own. In Hawaii there was the James Clerk Maxwell Telescope (JCMT) on Mauna Kea, a 15-meter dish. Today astronomers from China, Korea, Japan, and the Academia Sinica in Taipei, among others, work alongside each other at the JCMT. The two European telescopes operated by the Institut de Radioastronomie Millimétrique (IRAM) on Pico del Veleta in Spain and the Plateau de Bure in the French Alps were on firm footing and continued to be operated on a permanent basis. Other observatories were only in the planning phase, among them the Large Millimeter Telescope (LMT) in Mexico—ideally located for us, geographically speaking. It was supposed to be a 50-meter supertelescope, but the time when it was brought online was delayed until 2011, and even then it wasn’t completely finished. Even on the south pole a telescope specially built for cosmology was in the planning, which became operational in 2007. But it was another eight years before my colleague Dan Marrone from Arizona and his colleagues were able to successfully link up the telescope in the remoteness of Antarctica with a VLBI network.
  2. H. Falcke, et al., “Active Galactic Nuclei in Nearby Galaxies,” American Astronomical Society Meeting Abstracts 200 (2002): 51.06,…200.5106F.
  3. P. A. Shaver, “Prospects with ALMA,” in: R. Bender and A. Renzini, eds., The Mass of Galaxies at Low and High Redshift: Proceedings of the European Southern Observatory and Universitäts-Sternwarte München Workshop Held in Venice, Italy, 24–26 October 2001 (Springer-Verlag, 2003), 357,
  4. De Gelderlander, April 2003.
  5. G. C. Bower, et al., “Detection of the Intrinsic Size of Sagittarius A* Through Closure Amplitude Imaging,” Science 304 (2004): 704–8,…304..704B.
  6. S. Markoff, et al., eds., “GCNEWS–Galactic Center Newsletter,” vol. 18,
  7. The minutes are in my private archive. My Chilean colleague Neil Nagar also took part occasionally.
  8. Sheperd S. Doeleman, et al., “Event-Horizon-Scale Structure in the Supermassive Black Hole Candidate at the Galactic Centre,” Nature 455 (2008): 78–80,…78D.
  9. A Science Vision for European Astronomy (Garching: ASTRONET, 2010), 27.
  10. Sheperd Doeleman, et al., “Imaging an Event Horizon: submm-VLBI of a Super Massive Black Hole,” Astro2010: The Astronomy and Astrophysics Decadal Survey 68 (2009),
  11. Monika Mo ́scibrodzka, et al., “Radiative Models of SGR A* from GRMHD Simulations,” The Astrophysical Journal 706 (2009): 497–507,…706..497M.
  12. Monika Mo ́scibrodzka, Heino Falcke, Hotaka Shiokawa, and Charles F. Gammie, “Observational Appearance of Inefficient Accretion Flows and Jets in 3D GRMHD Simulations: Application to Sagittarius A*,” Astronomy and Astrophysics 570 (2014): A7,…570A…7M.
  13. Monika Mo ́scibrodzka, Heino Falcke, and Hotaka Shiokawa, “General Relativistic Magnetohydrodynamical Simulations of the Jet in M 87,” Astronomy and Astrophysics 586 (2016): A38,…586A..38M. But Dexter’s work, too, had already provided an excellent prediction based on GRMHD simulations: Jason Dexter, Jonathan C. McKinney, and Eric Agol, “The Size of the Jet Launching Region in M87,” Monthly Notices of the Royal Astronomical Society 421 (2012): 1517–28,
  14. In the end, because the chances were so bad, 50 percent fewer applications were submitted in our round, so the chances were actually 3 percent.
  15. Images and videos from our ERC project can be found at: C. Goddi, et al., “BlackHoleCam: Fundamental Physics of the Galactic Center,” International Journal of Modern Physics D 26 (2017): 1730001–239,
  16. R. P. Eatough, et al., “A Strong Magnetic Field Around the Supermassive Black Hole at the Centre of the Galaxy,” Nature 501 (2013): 391–94,
  17. Doctoral students: Michael Janßen (Lower Rhine), Sara Issaoun (Canada), Freek Roelofs, Jordy Davelaar, Thomas Bronzwaer, Christiaan Brinkerink (Netherlands), Raquel Fraga-Encinas (Spain), Shan Shan (China); postdoc: Cornelia Müller (Germany); senior scientists: Ciriaco Goddi (Italy), Monika Mos ́cibrodzka (Poland), Daan van Rossum (Germany); project manager: Remo Tilanus (Netherlands).
  18. L. D. Matthews, et al., “The ALMA Phasing System: A Beamforming Capability for Ultra-High-Resolution Science at (Sub)Millimeter Wavelengths,” Publications of the Astronomical Society of the Pacific 130 (2018): 015002,
  19. The idea for the melody probably came from chief operator Bob Moulton, but Tom Folkers, who wrote the operating system for the entire SMT, was the one who programmed it.
  20. Tweets and images from February 11, 2016, when after a thesis defense we watched the press conference for the LIGO/Virgo Collaboration in the auditorium at Radboud University:;
  21. Interview with Karsten Danzmann on Deutschlandfunk, February 12, 2016,
  22. Mickey Steijaert, “The Rising Star of Sara Issaoun,” Vox: Independent Radboud University Magazine, June 21, 2019,

Chapter 10 – Striking Out on Expedition

  1. See photo insert and glossary for the telescopes in the EHT experiment: ALMA and APEX in the Atacama Desert in Chile, SMT on Mount Graham in Arizona, the James Clerk Maxwell Telescope and the Submillimeter Array on Mauna Kea in Hawaii, the IRAM 30-meter Telescope on Pico del Veleta, the Large Millimeter Telescope (LMT) on the dormant volcano of Sierra Negra in Mexico, and the South Pole Telescope (SPT) at the Amundsen-Scott South Pole Station. The SPT cannot observe the M87 Galaxy because it is located in the northern part of the sky.
  2. Pink Floyd, “Comfortably Numb,” track 6 on The Wall, Harvest Records, 1979. Lyrics from:
  3. This time Michael Janßen goes to Mexico with computer scientist Katie Bouman from MIT. My Italian colleague Ciriaco Goddi travels with Geoff Crew from Haystack to ALMA in Chile. Remo Tilanus flies to Hawaii to work alongside Mareki Honma and other colleagues from Asia at the JCMT. Sara Issaoun again looks after the telescope in Arizona, along with Freek Roelofs and Junhan Kim, who had prepared the South Pole Telescope over Christmas.
  4. Peter Mezger was the director of the submillimeter wave group at the Max Planck Institute for Radioastronomy. His book Blick in das kalte Weltall was published in 1992 with the story of the telescopes, particularly the SMT/HHT.
  5. Thomas Krichbaum from Bonn and Rebecca Azulay, a young Spanish postdoc working at the MPI, along with the two Spaniards Pablo Torne and Salvador Sánchez from IRAM. Torne specializes in astronomical observation and Sánchez in the technical equipment. The station director Carsten Kramer was also there with us at the beginning.
  6. Actually two movies were made: The Edge of All We Know by Peter Galison of Harvard,, and How to See a Black Hole: The Universe’s Greatest Mystery by Henry Fraser, Windfall Films, both initiated by the Harvard Group.
  7. M. J. Valtonen, et al., “A Massive Binary Black-Hole System in OJ 287 and a Test of General Relativity,” Nature 452 (2008): 851–53,
  8. Andrew Nadolski was the second man at the south pole.
  9. Karl Schuster, director, IRAM.
  10. David Hughes, director of the LMT.
  11. Lizzie Wade, “Violence and Insecurity Threaten Mexican Telescopes,” Science, February 6, 2019,

Chapter 11 – An Image Resolves

  1. The calibration team includes Lindy Blackburn and Maciek Wielgus from Harvard University, Chi-kwan Chan from Arizona, my doctoral students Sara Issaoun and Michael Janßen, and Ilse van Bemmel from Dwingeloo.
  2. A. R. Thompson, J. M. Moran, and G. W. Swenson, Interferometry and Synthesis in Radio Astronomy, 3rd Edition, (Springer Verlag, 2017).
  3. Radboud Pipeline for the Calibration of High Angular Resolution Data: M. Janßen, et al., “rPICARD: A CASA-Based Calibration Pipeline for VLBI Data. Calibration and Imaging of 7mm VLBA Observations of the AGN Jet in M 87,” Astronomy and Astrophysics 626 (2019): A75,…626A..75J. The JIVE team under Mark Kettenis and Ilse van Bemmel also took part, along with Kazi Rygl and Elisabetta Liuzzo from Bologna.
  4. A young team led by Michael Johnson, Katie Bouman, and Kazunori Akiyama heads up the imaging group. Harvard PhD student Andrew Chael also takes part. On the European side, Thomas Krichbaum and José Luis Gómez from Spain also play a strong role. In all, more than fifty scientists are involved. Sara Issaoun is among them, and even the theorist Monika Mo ́scibrodzka tries her hand at imaging.
  5. Bouman and Johnson’s group at Harvard make up one team. I was in Team II with my PhD students Freek Roelofs, Michael Janßen, and Sara Issaoun. Thomas Krichbaum and José Luis Gómez from Spain and their colleagues made up the third team, which specialized on the CLEAN algorithm. A young group of our Asian colleagues under Keiichi Asada made up the fourth team.
  6. FITS: Flexible Image Transport System.
  7. H. Falcke, “How to Make the Invisible Visible” (lecture, TEDxRWTH Aachen, 2018),
  8. Images from the EHT imaging workshop at Harvard in 2017 can be found here:
  9. These are two “regularized maximum likelihood” (RML) methods (eht-imaging and SMILI) and the CLEAN algorithm.
  10. Chi-kwan Chan led a group to determine the color scale.
  11. Francis Reddy, “NASA Visualization Shows a Black Hole’s Warped World,” nasa .gov, September 25, 2019,
  12. EHT theory groups formed around Charles Gammie in Illinois, Ramesh Narayan at Harvard, Luciano Rezzolla in Frankfurt, and Monika Mo ́scibrodzka in Nijmegen.
  13. Under the leadership of Feryal Özel in Arizona, Keiichi Asada in Japan, Jason Dexter in Garching, and Avery Broderick at the Perimeter Institute in Canada. Meanwhile Christian Fromm from the BlackHoleCam team in Frankfurt developed a new “genetic algorithm” in order to estimate parameters of the black hole by comparing the images with simulations.
  14. Photos and videos from the collaboration meeting in November 2018 in Nijmegen:
  15. The EHT publication committee was led by Laurent Loinard from Mexico and my Dutch colleague Huib Jan van Langevelde, as well as Ramesh Narayan and John Wardle from the US.
  16. Yosuke Mizuno, et al., “The Current Ability to Test Theories of Gravity with Black Hole Shadows,” Nature Astronomy 2 (2018): 585–90,…2..585M.
  17. “UH Hilo Professor Names Black Hole Capturing World’s Attention,” press release, University of Hawai’i, April 10, 2019,
  18. Video zooming in on the black hole:
  19. Nik’s music video, with cellphone videos taken at the press conference and the black hole image: [Nik], “Wahrscheinlich” (music video), https:/
  20. The alert astroblogger was Daniel Fischer,—thanks! Also Ralf Nestler from Der Tagesspiegel notified us.

Chapter 12 – Beyond the Powers of Our Imagination

  1. L. L. Christensen, et al., “An Unprecedented Global Communications Campaign for the Event Horizon Telescope First Black Hole Image,” Communicating Astronomy with the Public Journal 26 (2019): 11,…26…11C.
  2. Google Doodle:
  3. Tim Elfrink, “Trolls Hijacked a Scientist’s Image to Attack Katie Bouman. They Picked the Wrong Astrophysicist,” The Washington Post, April 12, 2019,
  4. L. L. Christensen, et al., “An Unprecedented Global Communications Campaign.”
  5. Th. Rivinius, “A Naked-Eye Triple System with a Nonaccreting Black Hole in the Inner Binary,” Astronomy and Astrophysics 637 (2020): L3,…637L…3R.
  6. The diameter of the black hole is approximately 24 kilometers.
  7. The art history of the image of the black hole is the subject of a doctoral thesis by Emilie Skulberg at Cambridge.
  8. M. Backes, et al., “The Africa Millimetre Telescope,” Proceedings of the 4th Annual Conference on High Energy Astrophysics in Southern Africa (HEASA 2016): 29,
  9. Freek Roelofs, et al., “Simulations of Imaging the Event Horizon of Sagittarius A* from Space,” Astronomy and Astrophysics 625 (2019): A124,…625A.124R; Daniel C. M. Palumbo, et al., “Metrics and Motivations for Earth-Space VLBI: Time-Resolving Sgr A* with the Event Horizon Telescope,” The Astrophysical Journal 881 (2019): 62,…881…62P.

Chapter 13 – Beyond Einstein?

  1. Event Horizon Telescope Collaboration, et al., “First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole,” Astrophysical Journal Letters 875 (2019): L1,…875L…1E.
  2. The hypothesis that antimatter falls just the same as matter is currently being experimentally tested at CERN: Michael Irving, “Does Antimatter Fall Upwards? New CERN Gravity Experiments Aim to Get to the Bottom of the Matter,” New Atlas, November 5, 2018,
  3. Dennis Overbye, “How to Peer Through a Wormhole,” New York Times, November 13, 2019,
  4. For examples of information-based theories of gravity, see: Martijn Van Calmthout, “Tug of War Around Gravity,”, August 12, 2019,; Stephen Wolfram, “Finally We May Have a Path to the Fundamental Theory of Physics . . . and It’s Beautiful,” (blog),; Tom Campbell, et al., “On Testing the Simulation Theory,” International Journal of Quantum Foundations 3 (2017): 78–99,; M. Keulemans, “Leven we eigenlijk in een hologram? Het zou zomaar kunnen,” de Volkskrant, March 10, 2017,
  5. Actually if you stirred for an infinitely long time in a big bowl of alphabet soup, you could randomly produce a book, but there would be no way of telling that you had, and it would disappear again immediately—you’d have to stop at exactly the right moment. It’s more efficient to write a book than to wait for one to suddenly appear.
  6. Ethan Siegel, “Ask Ethan: What Was the Entropy of the Universe at the Big Bang?” Forbes, April 15, 2017,
  7. In quantum physics one describes the preservation of information in a quantum system, i.e., the development of its wave function, with the term unitarity and the process of measuring a quantum particle often as the collapse of the wave function. The “condition” of a quantum particle and/or its wave function only determines the probability with which a certain value is measured. Before every measurement of quantum particles, you can only precisely measure the most probable value—i.e., the mean value over several measurements. But once a value is measured, it remains constant until something else is measured. Multiple measurements thus change the values of particles.
  8. “Schwarze Löcher erinnern sich an ihre Opfer,” Spiegel Online, March 9, 2004,
  9. Even in isolated quantum systems without gravity, it could be that information is thermalized and becomes lost, if the calculations described in this article are correct: Maximilian Kiefer-Emmanouilidis, et al., “Evidence for Unbounded Growth of the Number Entropy in Many-Body Localized Phases,” Physical Review Letters 124 (2020): 243601,

Chapter 14 – Omniscience and Limitations

  1. Jeremiah 33:22 (KJV).
  2. John Horgan, The End of Science (New York: Little, Brown, 1997).
  3. Ethan Siegel, “No Galaxy Will Ever Truly Disappear, Even in a Universe with Dark Energy,” Forbes, March 4, 2020,
  4. Sam Harris, Free Will (New York: Free Press, 2012), 5 (Kindle version): “Free will is an illusion. Our wills are simply not of our own making. Thoughts and intentions emerge from background causes of which we are unaware and over which we exert no conscious control. We do not have the freedom we think we have. Free will is actually more than an illusion (or less), in that it cannot be made conceptually coherent. Either our wills are determined by prior causes and we are not responsible for them, or they are the product of chance and we are not responsible for them.”
  5. In this context scientists have also begun debating the concept of emergence.
  6. An example for readers versed in mathematics: I determine the frequency of a light wave in a flat space with the help of a Fourier transform. But this only provides an infinitely exact value if I integrate the wave from-∞ to +∞; then, for example, the Fourier transform of a sine function is the exact same as the delta function. If I have less time than eternity, then the frequency of even a perfect sine function is always imprecise. For the same reason I can only measure the point in time or the location of an event with infinite precision if I have an infinite amount of frequencies or wavelengths at my disposal. But because every event and every particle is always spatially and chronologically finite, it is also in fact always imprecise.
  7. Natalie Wolchover, “Does Time Really Flow?: New Clues Come from a Century- Old Approach to Math,” Quanta Magazine, April 7, 2020,
  8. Lawrence Krauss, A Universe from Nothing: Why There Is Something Rather than Nothing (New York: Atria Books, 2014): Pos. 104/3284 (Kindle version).
  9. For this reason the entropy at the beginning of the universe was actually lower than it is now, when energy and mass are widely distributed throughout space. Every individual star, planet, or person might seem more “orderly” than the Big Bang, but seen in the context of the entire universe that scarcely makes a difference. It’s like with the box full of toy blocks in the playroom: at the moment of the Big Bang everything was in a small box; now everything’s in a giant playroom. Even if you take a few of the blocks and build a nice little house here and there, the big picture is one of immense disorder.
  10. With the probable exception of “dark energy,” which could be an energy of empty space.
  11. Martin Rees, Just Six Numbers: The Deep Forces That Shape the Universe (New York: Basic Books, 2001).
  12. K. Landsman, “The Fine-Tuning Argument,” arXiv eprints (May 2015): 1505.05359,
  13. I would have liked to discuss the subject with him, but at least we can still read his thoughts on it: Stephen Hawking, Brief Answers to the Big Questions (London: John Murray, 2018).
  14. John 1:1. The verse reads, in full: “In the beginning was the Word, and the Word was with God, and the Word was God.” (KJV).
  15. Genesis 11:1–9, the building of the Tower of Babel. In this famous story God first has to descend in order to be able to look at the tower.
  16. 1 Corinthians 13:13 (Easy-to-Read Version), Paul’s song in praise of love.