2020 Nobel Prize for Physics: Black holes and the Milky Way's darkest secret
22020 Nobel Prize for Physics:Black holes and the Milky Way’s darkest secret
Joseph Samuel
1, 2 Raman Research Institute, Bangalore-560080, India International Center for theoretical Sciences,Tata Institute of Fundamental Research, Bangalore-560089, India (Dated: November 16, 2020)
Abstract
This article was written at the invitation of Current Science to explain the history and Sciencebehind this year’s Nobel prize in Physics. The article is aimed at a general audience and providesa popular account and perspective on the subject of black holes. a r X i v : . [ phy s i c s . pop - ph ] N ov . INTRODUCTION The Nobel Prize for physics this year was awarded jointly to Roger Penrose, ReinhardGenzel and Andrea Ghez. The prize recognises theoretical and experimental advances madein the physics and astronomy of black holes. Black holes have long fascinated the lay publicas well as scientists. They appear in our language, movies, sitcoms and science fiction.Scientists are obsessed with them as they lie at the edge of our current understanding of theUniverse. The scientists honoured by the prize have been instrumental in teasing out thedark secrets of these mysterious objects. There was a time that the very existence of blackholes was seriously doubted. With advances in science, technology and understanding, wenow realise that black holes are commonplace in the Universe. Every galaxy worth the namehas one. Indeed, there’s one right in our backyard, in the Milky Way. While their existenceis firmly established, black holes continue to throw up challenges to our understanding ofthe Universe. The physics and astronomy of black holes remains a vibrant field. The prizerecognises the advances which have already been made in this field and provides a stimulusfor those which are yet to come.Roger Penrose (b. 1931) is a theoretical and mathematical physicist at the Universityof Oxford, UK. He has done seminal work in Einstein’s General Theory of Relativity. Hehas also thought deeply about the foundations of quantum mechanics and its relation torelativity. His interests include the philosophy of science and its popularisation. He alsoenjoys recreational mathematics and shares his enthusiasm with the lay public. As hisdrawings on the blackboard and illustrations in his writings reveal, he is also no meanartist.Reinhard Genzel (b. 1952) is an astrophysicist at the Max Planck Institute for Extrater-restrial Physics, Garching near Munich. He also has affiliations with the Ludwig MaximillianUniversity in Munich and the University of California, Berkeley, USA.Andrea Ghez (b. 1965) is an astronomer at the University of California, Los Angeles,USA. She has devoted her life to understanding the center of our Galaxy, the milky way.She is the fourth woman to win the Nobel Prize in Physics.Half of the Nobel Prize is awarded to Roger Penrose and the other half shared betweenReinhard Genzel and Andrea Ghez.In the rest of this article we set this year’s prize in historical perspective, describe the2enesis of the idea of a black hole, the sustained scepticism that delayed wide acceptance ofthe idea, accumulation of experimental evidence for their reality and some of the challengesthat remain for fundamental physics and astronomy.
II. PREHISTORY OF BLACK HOLES
The idea of a black hole occurred independently to two polymaths- John Mitchell andPierre-Simon Laplace- separated in time by thirteen years and in space by the Englishchannel. John Mitchell was an English clergyman well versed in astronomy, geology, opticsand gravitation. He was working within the Newtonian scientific paradigms of his day: theNewtonian theory of gravity, corpuscular light and a geometric interpretation of mechanics.Mitchell (1783) based his reasoning [1] on the idea of escape speed, the speed needed fora projectile to escape to infinity from the surface of an astronomical object. This speed isabout 11 km/sec for the earth and about 600 km/sec for the Sun. These speeds are farless than the speed of light which travels at 300,000 km/sec. However, if there is a bodywith same density as the Sun and about 500 times its diameter, even light would not beable to escape. Thus, he concluded that the most massive bodies in the Universe may beinvisible! We may only be able to deduce their existence by their gravitational influence onother stars. To quote John Mitchell, “.. we could have no information from light; If anyother luminous bodies would happen to revolve around them we might still perhaps from themotions of these revolving bodies infer the existence of the central ones with some degree ofprobability.” As we will see below, this is precisely what has been done by the astronomersGenzel and Ghez of this year’s prize.The same idea was independently conceived [2] in France by Pierre-Simon de Laplace in1796. Laplace, sometimes called the French Newton, worked on topics as diverse as astron-omy, probability, surface tension and the origin of the solar system. In his “The System ofthe world” he stated: “Therefore there exists, in the immensity of space, opaque bodies asconsiderable in magnitude and perhaps as equally numerous as the stars”. Laplace’s argu-ments were mathematically more sophisticated than his contemporaries, using differentialcalculus in contrast to the geometric arguments of John Mitchell. But the content was thesame: the Universe may contain “dark stars”. Or in Laplace’s words, “The largest bodiesin the Universe may well be invisible by reason of their magnitude”.3hese prescient speculations lay in obscurity for over a century and were only revived inthe 20th Century with Einstein’s General Theory of Relativity.
III. BLACK HOLES IN GENERAL RELATIVITY: AN IDEA DELAYED
In 1915, Einstein proposed his General Theory of Relativity (GTR) which explainedgravitation as the curvature of spacetime. In about a month, Karl Schwarzschild discovered[3] the most elementary solution of Einstein’s equations, which described the sphericallysymmetric gravitational field of a point mass M . The solution had the feature that thecurvature grew without bound as one approached the centre of symmetry, a feature thatmathematicians describe as a “singularity”. This was not entirely unexpected. The New-tonian gravitational field of a point mass also grows without bound as one approaches thecentre of symmetry. However, there was also something intriguing happening at a finiteradius r = GMc , where G is Newton’s gravitational constant and c the speed of light. Thiswas not properly understood at the time. Some of the expressions describing the geometryseemed to vanish and others to blow up, evading a clear physical interpretation. Thereseemed to be some confusion between space and time at this “Schwarzschild radius”. Re-searchers named it the Schwarzschild “Singularity” and moved on. They could afford to doso. In any known astronomical body, the problem did not appear, as the Schwarzschild sin-gularity was deep inside the body, where the vacuum Schwarzschild solution did not apply.For instance, the Schwarzschild radius of the Earth is 1 cm and that of the Sun is 3 km. Theproblem would only appear if the body collapses gravitationally to within its Schwarzschildradius. This means squeezing the earth to within the size of a marble. Or the Sun to withinthe size of a small town.In due course, the problem did appear. Arthur Eddington was a renowned astronomerat Cambridge who worked on the life and death of stars. It was known then that starsshine by burning nuclear fuel in their cores. The heat released in these reactions causesmolecular motions and generates pressure which supports the star against its own gravity.Over millions of years the star shines and exhausts its nuclear fuel. It then cools and inthe absence of thermal molecular motions, contracts under its own gravity. A star with themass of the Sun would contract till it becomes a White dwarf, a star not much bigger thanthe Earth, which is supported by the quantum mechanical motions of electrons required by4he uncertainty principle. Eddington and most of his contemporaries believed that spentstars would find their final repose as white dwarfs.This peaceful state of affairs was disturbed by a young Indian, a graduate of Presi-dency college, Madras who was then working in Cambridge: Subrahmanyam Chandrasekhar.Chandrasekhar applied himself to understand the equilibrium of White dwarfs. In 1931, hediscovered that as the mass of the star gets bigger, the electrons have to move faster andfaster to exert enough pressure to counteract gravity. However, the motion of electrons islimited by the speed of light and if the mass of the star exceeds 1.4 times the solar mass,gravity wins out and the white dwarf is unstable to gravitational collapse. Eddington refusedto believe this conclusion. He did not have a scientific argument against Chandrasekhar’sreasoning, but only a conviction that “Nature could not behave in this absurd fashion”!Nevertheless, Eddington’s eminence and authority prevailed and the idea of a black hole layon the shelf for a few more years.Was there any force that could stop this gravitational collapse? The answer came in thelate nineteen thirties. A paper in 1938 in Zeitschrift [4] f¨ur Physik by B. Datt, Presidencycollege Calcutta, gave general solutions of Einstein’s equations in spherical symmetry. Dattwas more interested in the cosmological context, but the paper was noticed by the Russianschool around L.D. Landau. Viewed in time reverse, these cosmological solutions can beinterpreted as the interior view of gravitational collapse. Oppenheimer and Snyder (1939) atthe University of California, Berkeley found solutions [5] of Einstein’s equations that showedthat a collapsing star would continue to collapse past its Schwarzschild radius. Oppenheimerand Snyder clearly interpret their equations: “The star thus tends to close itself off fromany communication with a distant observer; only its gravitational field persists. ” Theyhad correctly identified the event horizon of a black hole. The conclusion was right but thetiming was poor. Shortly afterwards, World War II broke out. Scientific research projectswere shelved in favour of the urgent demands of the war effort. Many scientists were involvedin the war effort, some of them developing radar to detect enemy planes. Oppenheimerdropped his research on gravitational collapse and went on to lead the Manhattan project.Another delay!Even in 1939, Einstein was unconvinced by the physical reality of the Schwarzschild ra-dius. Writing in the Annals of Mathematics in 1939, he argued that time would standstill at the Schwarzschild radius, a patently absurd conclusion. Also bodies falling into the5chwarzschild radius would appear to hover at the Schwarzschild radius, frozen in time forever. He seriously doubted that these predictions of his theory had any physical validity. Hebelieved that these absurdities were artefacts of the idealisation involved in a point mass.After the famous point mass solution, Schwarzschild had in fact discovered a interior spher-ically symmetric solution of Einstein’s equations. But as Schwarzschild had assumed anincompressible fluid interior, Einstein was able to dismiss this too as an artefact of unrea-sonable assumptions: in an incompressible fluid, sound would propagate instantaneously,violating relativity.The high degree of symmetry of the Oppenheimer-Snyder collapsing solution was alsoa matter of concern. Perhaps the collapse and resultant singularity was a consequence ofthe artificial initial conditions. Perhaps deviations from spherical symmetry would preventgravitational collapse. Maybe the matter would “bounce back” due to other interactions,or release its energy in a burst of gravitational radiation. Many cosmological solutions ofEinstein’s equations were known. Most of these had singularities either in the past or inthe future. Naturally, all the solutions found analytically had a high degree of symmetry,since Einstein’s equations are hard to solve without the simplifying assumption of symmetry.The question remained: are total gravitational collapse and singularities generic in GeneralRelativity? IV. RADIO ASTRONOMY AND RELATIVISTIC ASTROPHYSICS
After the war, the world was beating its swords into ploughshares. Radio engineers turnedtheir war-time instruments to the skies and discovered a whole new window to the Universe.Unlike light, radio waves are not absorbed by dust in the Galaxy and radio telescopes wereable to “see” clear and deep into the cosmic distance. Radio waves were detected fromthe Milky Way and from other galaxies. A new branch of astronomy was born. As theobservations mounted, radio astronomers realised that the skies were not as placid as theyappeared. Radio waves were emanating from very tiny regions in the sky. The size of theemitting region had to be less than a light day since the intensity sometimes changed in afew hours. But the spectral lines of these sources showed that they had to be at an enormouscosmic distance. From the energy received at the telescopes, it was clear that some of thesepoint like “stars” were shining brighter than whole galaxies. They were called quasars or6uasi-stellar objects (QSOs) or Active Galactic Nucleii (AGN). Many sources had radiojets, matter ejected at relativistic speeds from the centre (Fig.1). There were violent andenergetic events taking place at the centers of galaxies. Tremendous amounts of energy werebeing released from an object not much larger than our solar system.
FIG. 1: Figure shows an artist’s impression of a black hole surrounded by an accretion disc emittinga radio jet. Figure Credit © Roshni Rebecca Samuel
What was the source of this energy? Nuclear energy was an unlikely candidate. Nuclearreactions have about a one percent efficiency in converting mass into energy ( E = mc !). Itwould need enormous amounts of matter to be concentrated into a tiny volume in order toexplain the observed energy output. Such concentrations of matter would actually signal asituation close to gravitational collapse. In such compact objects, the gravitational energyof falling matter could be converted into radiation with an efficiency as high as five percent(for a non rotating black hole). As more data came in, it was clear that many galaxies hadcompact objects in their cores. Relativistic astrophysics was born. The Texas symposiumin 1963 marked a coming together of mathematics, Physics and astronomical observations.7 . RELATIVITY AFTER EINSTEIN The period after Einstein’s death in 1955 marked a new phase in the development ofgeneral relativity. This was the beginning of mathematical relativity. Much of the earlierconfusion with “Singularities” stemmed from the fact that researchers were not sufficientlysophisticated mathematically. They had an undue faith in the coordinates they used todescribe space and time. Some “singularities” are only apparent; they are failures of thecoordinate system not features of the spacetime. This is best explained by using geography.Over the Earth, we use latitudes and longitudes to pin point locations. However, thismethod fails at the poles of the Earth, as the longitude is ill defined.But there is nothingspecial about the poles. This is a removable singularity, a failure of the coordinate systemrather than an intrinsic feature of the Earth. What was needed was an appreciation ofglobal methods, which mathematicians had developed for their own purposes. By patchingtogether local descriptions using coordinates, they were able to arrive at a global notion:that of a manifold. With increased sophistication, it becomes clear that the Schwarzschild“singularity” is only apparent. There is something funny happening at the Schwarzschildradius, but it is not a singularity. It is the event horizon of a black hole!In the year of Einstein’s death in 1955, Amal Kumar Raychaudhuri, working in Calcutta,studied the motion of a cloud of dust in general relativity and derived an equation ([6]) theRaychaudhuri equation) which was to prove central in further developments. The equationexpresses the attractive nature of gravity: that neighbouring particle trajectories would tendto focus. Slightly later, a version of the Raychaudhuri equation was independently derivedby L. D. Landau in the Soviet Union. Two of his colleagues, E.M Lifshitz and I.M Kha-latnikov studied [7] the question of whether singularities were generic in general relativity.Their conclusion was negative: singularities were artefacts of symmetry and did not appeargenerically in the theory. Roger Penrose was very sceptical of this conclusion. In seminalpapers, he applied the Raychaudhuri equation, using some global mathematical techniquesfrom differential topology and geometry to arrive [8] at the opposite conclusion: genericsolutions of Einstein’s equations contain singularities either in the past (like the big bang)or in the future (as in the centre of a black hole). One of the key ideas he introduced was theglobal notion of a trapped surface. Imagine a sphere in ordinary space emitting a flash oflight. One part of the wave emanating from the sphere moves into the sphere contracts ev-8rywhere and decreases in area. The other wave moves out, expands everywhere, increasingin area. In some gravitational fields, like that inside the Schwarzschild radius, it can happenthat both these waves (or wave fronts more precisely) are contracting everywhere. This iswhat Penrose calls a trapped surface. Once a trapped surface forms, Penrose showed thatcollapse and singularities are inevitable. Small perturbations of the trapped surface in theSchwarzschild spacetime do not destroy the trapped surface and it follows that singularitiesare generic. More precisely, what he showed was that the spacetime was incomplete. Insuch a spacetime, photon trajectories would abruptly terminate, suggesting that points ofspacetime have been artificially removed from consideration. Putting them back reveals thesingularity. One of the key assumptions in the theorem was that matter was “reasonable” i.e there was no negative mass, which is the case with all known forms of matter. Sub-sequent work by Penrose and Hawking nailed it even more firmly: most spacetimes havesingularities, either in the past or in the future. VI. A BLACKHOLE IN OUR BACKYARD
The Nobel prize was awarded for work by two independent groups, who studied thecentral region of our Galaxy over a period of twenty years and adduced strong evidence forthe existence of a black hole in the centre of our Galaxy. The estimated mass of the blackhole is 4 . km (40 light seconds). The evidence is based on the observations of the motion ofstars in a small region near the center of the Milky way. The observations tell us that thestars are in orbit around a massive central object. The motion is consistent with Kepler’slaws of planetary motion. The center of the Galaxy is 24,000 light years away from us. Atthis distance, the motion of stars appears as a very tiny angular change in the position ofthe star in the sky. Astronomers refer to this as “proper motion”. Detecting the propermotion is a challenging task. First, one needs to build up a celestial reference frame againstwhich proper motions can be measured and followed over decades. One also needs fineangular resolution to distinguish objects in the field of view. In analogy one needs to beable to distinguish between the left and right eye of a man standing 250 kilometers away.The angular resolution of a telescope increases with its size and with its operating frequency.(The best angular resolution one can get with a telescope of size D operating at a wavelength9 is λD in radians.) Even with large telescopes operating at small wavelengths, there is aproblem because the turbulence in the earth’s atmosphere blurs and distorts the image.The two groups (one led by Genzel and the other by Ghez), studied the region around thesource Sagittarius A ∗ near the centre of our Galaxy. This region has fast moving stars andhot ionised gas. The region of interest subtends an angle of only 6 (cid:48)(cid:48) (six arc seconds; one arcsecond is 1 / . µ m is a twentieth of an arcsecond. This is called the diffraction limit. The diffraction limit is hard to achieve becauseof the turbulent atmosphere, which causes the image to shift on time scales of the orderof a second. To beat this problem, the observers used advanced techniques made possibleby modern technology. CCD (Charge coupled devices) enabled larger detector efficiencythan the older photographic plates, permitting shorter exposures. The observations weremade with short exposures (about a tenth of a second). Over this timescale, the atmospherecan be regarded as frozen. The snapshots can then be subject to speckle imaging. Inthe most basic version, the successive images are combined with a compensatory shift. Amore advanced version called speckle interferometry uses Fourier analysis to produce a highresolution image. Another technique used in imaging is adaptive optics. This methodmeasures the atmospheric fluctuations in real time and corrects for the distortion of theimage. The atmospheric fluctuations have the effect of corrugating the plane wavefrontreceived from the astronomical source. These corrugations are compensated by having adeformable mirror adapting to cancel the distortion. Early efforts used a ‘guide star”: areference star whose apparent position reveals the fluctuations of the atmosphere. A moreadvance version uses a laser to create an artificial guide star in the sky which is used as areference.By patient observations [9], [10]lasting over decades, the astronomers were able to identifystars orbiting around a central massive object. They were able to observe the motion of thestars in their orbit and even complete orbits. Some of the orbits are extremely elliptical andin the closest approach complete orbits. Some of the orbits are extremely elliptical and inthe closest approach to the central object give us a weak upper bound on its size. One of thestars has a period of just fifteen years, well within the patience and lifetimes of astronomers.The stars can be adequately described by Newtonian gravity. Kepler’s laws tell us that10n the solar system, planets move in elliptical orbits. What the observers see (Fig.2) at thecentre of our Galaxy is exactly the same, except that it is scaled up in size. The Sun isreplaced by the central black hole, which is 4 Million times the mass of the Sun. The planetsare replaced by stars traversing elliptical orbits. Tracing the orbits of the stars, measuringtheir positions and velocities tells us the mass of the central object as well as an upper boundon its size. Nothing fits the bill like a black hole. VII. CONCLUSION
This year’s Nobel prize clearly brings out the interaction between theory and experi-ment in this area of physics. The speculations of Mitchell and Laplace and their illustrioussuccessors were all purely theoretical. It was only with the coming of Radio astronomy inthe 1950’s that experimental evidence began to emerge. The radio observations of Activegalactic nucleii showed that many galaxies have black holes in their centres. The questionnaturally arose: does the Milky way have one? Today we not only know the Milky wayharbours a black hole, we have measured its mass! The day is not far off when we will alsoknow its spin! The experiments now throw up new challenges for the theory of galacticevolution. Black holes are believed to be important in the evolution of galaxies. The obser-vations reveal that there are a surprising number of young stars in the vicinity of the blackhole. One would not have expected this, as black holes tend to tidally disrupt large objectslike the gas clouds which form young stars.The singularity theorems are important developments in Relativity in its modern phase.Apart from telling us clearly that general relativity predicts black holes, they also tell usthat general relativity will fail at some point. A new theory will be needed to understand thesingularity. Understanding black holes has also given us hints about the new direction. Theirreversible nature of gravitational collapse is reminiscent of other irreversible phenomenain physics like the increase of entropy and the loss of information. Work by Hawking in the1970s revealed that black holes are thermal objects in quantum physics. It seems very likelythat the missing piece of this puzzle is a quantum theory of gravity. This is the holy grailof theoretical physics. 11
III. ACKNOWLEDGEMENTS
I thank Roshni Rebecca Samuel for her artistic drawing of a black hole in Figure 1 andfor the portraits of the prize winners in Figure 3-5; and Rajaram Nityananda, LakshmiSaripalli, Biman Nath, Supurna Sinha, Ravi Subrahmanyan and Sukanya Sinha for readingthrough this article and suggesting improvements. [1] J. Mitchell , Philosophical Transactions of the Royal Society (1784).[2] P. S. Laplace , Exposition du Systeme du Monde (1796).[3] K. Schwarzschild , Sitzungsberichte der Koniglich Preussischen Akademie der Wissenschaften , 189 (1916).[4] B. Datt, Zeitschrift f¨ur Physik , 314 (1938), URL https://doi.org/10.1007/BF01374951 .[5] J. R. Oppenheimer and H. Snyder, Phys. Rev. , 455 (1939), URL https://link.aps.org/doi/10.1103/PhysRev.56.455 .[6] A. Raychaudhuri, Phys. Rev. , 1123 (1955), URL https://link.aps.org/doi/10.1103/PhysRev.98.1123 .[7] E. Lifshitz and I. Khalatnikov, Advances in Physics , 185 (1963),https://doi.org/10.1080/00018736300101283, URL https://doi.org/10.1080/00018736300101283 .[8] R. Penrose, Phys. Rev. Lett. , 57 (1965), URL https://link.aps.org/doi/10.1103/PhysRevLett.14.57 .[9] R. Genzel, F. Eisenhauer, and S. Gillessen, Rev. Mod. Phys. , 3121 (2010), URL https://link.aps.org/doi/10.1103/RevModPhys.82.3121 .[10] A. M. Ghez, S. Salim, S. D. Hornstein, A. Tanner, J. R. Lu, M. Morris, E. E. Becklin, andG. Duchene, The Astrophysical Journal , 744 (2005), URL https://doi.org/10.1086%2F427175 . S8 S13S1S12S14
Astronomers were able to map an entire orbit of less than 16 years for one of the stars,S2 (or S-O2). The closest it came to Sagitta-rius A* was about 17 light hours (more than1000 million kilometres).
The stars’ orbits are the most convincing evidence yet that a supermassive black hole is hiding in Sagittarius A*. This black hole is estimated to weigh about 4 million solar masses, squeezed into a region no bigger than our solar system.
Stars closest to the centre of the Milky Way
The S2 star’s radial velocity increases as it approaches Sagittarius A* and decreases as it moves away along its elliptical orbit. Radial velocity is the component of the star’s velocity that is in our line of sight.Some of the measured orbits of stars close to Sagittarius A* at the centre of the Milky Way. Closest to Sagittarius A* (in 2002 and 2018), S2 reaches its maximum velocity of 7 000 km/s.Astronomers startedmapping the path ofS2 in 1992. S2 S2 RADIAL VELOCITY S2 Sagittarius A* Sagittarius A* R a d i a l v e l o c i t y ( k m / s )
400 AU60 billion km©Johan Jarnestad/The Royal Swedish Academy of Sciences