Looking at Nothing: Investigating The Lights from a Black Hole
Review
Ranadeep Ghosh Dastidar
Being one of the most advanced theories of its time, (and its past) general theory of relativity (GTR) was viewed as a fundamental necessity to account for the discrepancies in Newtonian gravity. Trying to account for the changing precession of Mercury, Einstein’s theory ended up unleashing hidden (quite literally) monsters in the extreme gravity. Black holes being probably the most famous example of that. Since the first theoretical proposition of a black hole through GTR, attempts to realize them theoretically and probe observationally, have more often than not raised more questions than answers. However, its journey of a century now, from 1919 to 2020 has paved way for milestones impacting the very foundations of Physics. This year, the Royal Swedish Academy of Sciences decided to award the Nobel Prize to two such milestones, for the proof of the theory of the very existence of the black hole and ingenious methods to observe them.
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Our whole universe was in a hot, dense state
Then nearly fourteen billion years ago expansion started, wait. . .
Wasn’t it only last year the Royal Swedish Academy of Sciences started their Nobel Prize in Physics announcement with the title track of ‘The Big Bang Theory’ - a popular Television sitcom,, in the mood of it being awarded to physical cosmology and exoplanets?! And yet again the very next year it was again awarded in the subtopic of cosmology and astrophysics. A field which attracted 3.5 Nobles from 1901 to 2000, and already 6 since 2001-2020. Drawing parallels with the show, Prof. Andrea Ghez as the real-life Amy Farrah Fowler becomes only the fourth woman in Physics to be awarded the Nobel Prize. While this year it’s remarkable to see the theory and its observation bagging the award together, it also makes the fraction of female laureates in Physics 1.9% (4 of 216 winners)[1]. While hopefully, the long-running trend of "same old white men" dominating the prizes is diversifying, the trend towards cosmology and astrophysics is getting stronger. While the other fields may not be fancying this, why is it that three awards in the past four years have something or the other to do with “Black Holes".
It was in the trenches somewhere in the eastern front of Germany, the director of the Astrophysical Observatory in Potsdam, serving as an artillery lieutenant, Karl Schwarzschild came across the recently proposed theory of gravitation only a few months back, in November 2015. In only a couple of months, Schwarzschild would write back to Einstein, giving the first-ever formal and exact solution to his field equation. Contrary to Einstein’s beliefs, who considered his field equation for gravity could not be solved exactly, Schwarzschild had proposed a solution for a rather “boring” system - ‘how do space and time behave around a spherical, non-charged, non rotating massive object’. While this showed that exact solutions to Einstein’s Field Equation do exist, perhaps the biggest implication of it was what happens when that plain and simple object becomes very heavy (say few tens of solar masses), such that the escape velocity from it is more than the speed of light. In fact, any object having finite mass, Schwarzschild’s solution, a geometric one (Schwarzschild metric), predicted the existence of a spherical boundary centered around it, at rs = 2GM/c2 from the center of the object of mass M, within which the gravitational pull is so high that not even light could escape from it, the event horizon. But, for most of our daily massive objects, such a radius is negligible (often less than Planck length), to put things in perspective, if our own Earth was to become so dense it has to be compressed to the side of a peanut!! In the stellar perspective however a large M allows for a more formidable rs, formerly known as “frozen stars'', these bizarre objects would eventually be called “Black Hole”, a term coined in confusion by John Wheeler in 1967. Schwarzschild’s ’boring system’ solution was soon followed by solutions of Einstein’s field equation for space around a charged massive object (Hans Reissner and Gunnar Nordström, 1916-18), rotating object (Roy P. Kerr, 1963), and eventually charged-rotating massive objects (Roy Kerr and Ezra Newman, 1965). These were just the tip of an iceberg (or rather the entire Antarctic) for a field which would go on to fascinate Physicists and awe people, probably even beyond our lifetime.
Figure 1: Amal Kumar Roychoudhari carrying Proger Penrose and Stephen Hawking on his shoulder. In honour of Roychoudhuri equation for basis of Penrose-Hawking singularity, Ref. Sayan Kar, Resonance 2008.
Until the late 1950s, Schwarzschild’s solution and others were received with much criticism for it contained ’singularities’ when describing massive dense objects. Risking cliché, a very generic and crude way to visualise singularities is assuming it to be holes through a paper (yeah yeah, seen a million times in sci-fi). What Schwarzschild and others before 1960 proposed had two such tears through paper, one at the very center of the object and the other at the boundary of 'no light escape’ or better known as the event horizon of an ob ject. This for Schwarzschild’s solution lies at a radius of rs from the center of the object. While mathematically perfect and beautiful, singularities are mind-boggling nightmares for Physics. For the simple fact that, all laws of Physics can be expressed as differential equations, and calculus 101 teaches us they make sense only over continuous space (or space-time to be rigorous) and tears through pages aren’t quite that favorable. So for Physics and Physicists, all hell breaks loose when they encounter singularities, and skepticism to black holes as described by Schwarzschild, Reissner-Nordstr¨om is understandable. All until the 1960s, a decade which proved to be quite the game-changer for black holes, both theoretically and observationally. Kruskal and Szekeres in the 1960[2], would eventually go on to show that the event horizon singularity arising in Schwarzschild metric was due to a bad choice of coordinate system. In an impressive turn of events, using a hyperbolic coordinate transformation they discovered a single piece of coordinate system in which the space-time around a black hole could be described through continuous and differentiable coordinates, both inside and outside the event horizon. Thus proving the existence of event horizon is not a singularity but a very real boundary!! But what they still failed at was, their new coordinate system still could not account for the other singularity a the very center of black holes (at r = 0, if you may wish). Here comes in the picture our very own city boy from Kolkata (then Calcutta), Prof. Amal Kumar Raychoudhari (commonly called AKR). Working very reluctantly on properties of metal, AKR was always passionate about maths and deeply fascinated by general theory of relativity. Known lesser as one of the early proponents of Big Bang Theory, AKR’s biggest contribution to GTR was the very famous Raychaudhuri Equation[3]
θ,µvµ − aµ;µ + ⅓θ2 + 2(σ2 − w2) = Rµνvµvν.
Published first in 1955, this equation was independently discovered also by the very famous Lev Landau and would go on to change how physicists viewed singularities forever. In a nutshell what this equation says is that, if we consider multiple balls (or dust) traveling directly towards the center of a black hole from multiple directions, all of them can not but converge to a single point at the very center of it. But what the outstanding feature of this was, unlike its successors, the Raychaudhuri equation is a coordinate independent solution for the most generalised mass distribution. Thus contrary to, say, Schwarzschild metric event horizon, this converging point is not a coordinate singularity (one which can be done away with a different choice of coordinates), but a physical (real) one indeed. While Roychoudhari dealt only with dust (non-interacting), it lacked a key ingredient which collapsing masses or stars had, pressure. A star undergoing collapse due to its own gravity is expected to shrink in size, eventually becoming a dense ball of matter, so dense that all its atoms and particles are ripped apart to their constituent neutrons, aptly called neutron stars. Yet another genius and Nobel laureate of Indian origin, back in 1930, however showed that even if after the collapse, such a neutron star was to weigh more than 1.4 times the mass of sun gravity shall further overpower the pressure from neutrons that holds the shape of the star. This limit in his honour (as you already guessed) is called the Chandrasekar limit.
Figure 2: The various basic characteristics of a black hole. Penrose was the first to show that singularity is a physical necessity for a black hole. The accretion disk and relativistic jets are two very prominent energy sources detectable from near a black hole. Source: ESO
Thus, for a massive star undergoing collapse, we not only need to consider its trajectory but also the thermodynamics of it. This is where the brilliance of Roger Penrose kicks in (1965), building on Raychaudhuri equation, and generalised form on Einstein field equation including thermodynamic effects he showed that, if the space is infinite, and light becomes trapped inside a bounded region, a singularity is inevitable within it. In other words, if any particle was to enter such a bounded region, its trajectory over space and time would eventually blow up or become undefined eventually. And lo and behold, a collapsing star with more than 1.4 solar masses provides just the boundary, in the form of an event horizon in a very real universe. Penrose’s close buddy and an other genius beyond limits, Stephen William Hawking would build on this and go on to show for a finite space, all particles must eventually trace back to one single point in space and time, maybe a bang?! This theory eventually would merge and come to be known as the Penrose-Hawking singularity theorem. While Hawking showed one of the biggest revelations of GTR, the Big Bang, Penrose had indeed shown ”that black hole formation is a robust prediction of the general theory of relativity”. Maybe in a fantasy world, Hawking and AKR were still alive and possibly shared the 2020 Nobel Prize with Penrose. But, for fact, this year holds another beauty when theory and observation shared the prize.
Figure 3: Orbits of some of the closest star orbiting the supermas sive compact object, a blackhole Sagittarius A* at the center of milky way galaxy. Source: observations by Galactic Center Group, Keck tele scope/UCLA.
The 1960s was not only a theoretician’s paradise, around the 1950s and early ’60s (1963 to be precise) the all-sky radio survey, an effort by the European observatories to map the sky for objects in the radio frequency, noted a distinguished bright source ’3C 48’. What was fascinating was this radio source object seemed to be invisible in the optical sky, meaning the visible spectrum. By the end of the decade, hundreds more like it would be added to that list. Maarten Schmidt, a dutch astronomer observing 3C 48 using the Hale Telescope in the United States and Parkes Radio Telescope in Australia, was able to finally obtain a visible counterpart and its optical spectrum. While optical spectrums were supposed to yield the constituents of an astronomical source, hence its redshift (or blueshift) compared to on Earth spectrum of those elements and eventually the distance of the objects. 3C 48 was set to follow an entirely different course. An object which was surely a stellar object (star-like thingy), did not constitute any known element ever found in a star. Even if it did, the rate at which it was receding (redshift in the spectrum) was way beyond anything else ever observed. Further interferometric observations revealed, not only was it brighter than any galaxy (yes, the entire galaxy!!) ever observed, it was smaller than 1 light-year in size. They were hence called quasi-stellar objects, or a more familiar nickname ’Quasar’. Only a theoretical fantasy then, the most accepted explanation we know today was given pretty soon in 1964 by Edwin Salpeter and Yakov Zal’dovic. Supermassive black holes at the center of a galaxy feeding in on its nearby stars, or what’s technically called accretion disks. The feeding is so violent and gigantic, that it would emit radiations of energy in the radio frequency, energy more than any physical explanation ever perceived of, some a thousand times more than that of our entire galaxy!! While theoreticians were gradually packing up to understand a single black hole of a few tens of solar masses, here we already had observed supermassive black holes ranging from a few million to some hundreds of millions solar masses size.
After innumerous observations in radio and optical frequency, using some of the very famous observations like the deep field image from Hubble Space Telescope, we now know that most (if not all) galactic centers have such supermassive black holes at their centers, some feeding actively and some not so much. Our own Milkyway is no exception, falling in the former category, a supermassive compact radio source in the night sky. Observed first at the National Radio Astronomy Observatory, United States, found near the star Sagittarius, named aptly by one of its first observers, astronomer Robert Brown because the radio source was ’exciting’, Sagittarius A*[4]. Thus, it became the nearest and the most obvious source to look at and study. But how do you ”look at” something like a black hole, which you can’t see? Well, you obviously don’t. Further unlike quasars, Sagittarius A* is not an active galactic nucleus and hence we do not have the luxury to study its accretion disk too. What’s studied is its presence, the impact of the supermassive black hole on its nearby visible stars at the center of our galaxy. As pain staking as it sounds, thousands of stars at the center of our Milky way are studied, and most of them individually, one by one. Two rival groups who pioneered this mammoth task made quite an impact. One led by Prof. Andrea Ghez at the University of California, Los Angeles, and the other, an alumnus of the same university, Prof. Reinhard Genzel, director Max Planck Institute of Extraterrestrial Physics, Germany. Although having access to two of the best telescopes in the world, Keck Observatory in Hawaii (Ghez group) and Very Large Telescope (very honest name!) in Chile (Genzel group), the task was not as straightforward. Just like any photograph, astronomical observations are victims of blur rings. Imaging the very center of the galaxy was hard enough, even for the best telescopes, but the images further blurred due to continuously changing Earth’s atmosphere. To start with, Genzel used a well known and standard technique, called speckle imaging. Wherein, multiple snapshots of the same data were superimposed to avoid the blurring caused by Earth’s atmosphere. Later, both would move on to a very innovative observational technique called adaptive optics. A laser pointed to infinity, originating at the observatory, serves as what you may call a pseudo star. Since the disruptions in this pseudo star due to atmosphere, can be accurately tracked by the laser pointer corrections, the same corrections are implemented for an observed star. this enhanced the observations many folds.
Figure 4: We are in the golden age of astrophysics and cosmology. Top left, an artist’s impression of a direct image of Sagittarius A*. Top right, artist’s impression of two neutron star mergering, detected in 2017. Bottom, a huge missing part of the puzzle is black holes of thousands of solar mass range, existance of which was hinted just this year.
In Prof. Genzel’s word, the two did not have a particularly friendly relationship[5], but the rivalry achieved something very much desired, two groups arriving at the same results independently. One of the striking observations made by both was a star, orbiting ”nothing” with a 16 year time period at 2.55% the speed of light. Around the end of last decade, working independently the German group reported the mass of this supermassive black hole to be 4.21 ±0.38 million solar masses, the American counterparts reported a 3.7 ± 0.2 million solar masses, all confined in a 44 million kilometer diameter. To put in perspective, around 4 million suns compressed in a sphere having a diameter less than the distance from Earth to Mars. A truly supermassive compact object at the center of our galaxy indeed.
While it may seem it is about time for the oldest branch of science to put to rest. It’s only recently more and more breakthroughs are coming. It was only 2015 when we heard what the tune of gravity sounds like, gravitational ripples spreading like waves creating an entirely new branch of Gravitational Wave Astronomy. Only a couple of years back when, for the first time ever, we heard the waves and saw the act of the same astronomical event when two neutron stars merged. Only last year, when we photographed a real black hole in action, and only this year, when we got hints about intermediate-mass black holes (heavier than Schwarzschild and Penrose’s, lighter than Andrea and Reinhard’s). It is only now, the modern telescopes let us see way way more than we already expect. So when we look up at the sky, we always have more questions than answers.
Bibliography
I am Ranadeep Ghosh Dastidar, most commonly known as Rana. I graduated from IISERk this year itself, completing my MS thesis at CESSI, and currently a first-year graduate student at Purdue University in the United States. While I like research, my predilection for the fancy popularistic Physics words is more (hence got carried away by the starts and stuff). I hate to read but love to speak. So nonstop talking gives the greatest satisfaction, followed very closely by cooking and eating. My academic interests on the other hand lie with astrophysics, which lets me speak a lot, travel and manage my own time in the name of sky observations.
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