Naomi C. Robertson
A black hole is region of space where the gravitational pull is so strong that light is unable to escape. Since no light can escape, we are not able to observe black holes directly. The physicist John Wheeler (Figure 1) is often credited with being the first to coin the term black hole in 1969; however, the concept dates back much further to the Reverend John Michell (Figure 2), who hypothesized the existence of a “dark star” in 1783. It took until the 1960s for the idea of black holes to gain any observational support but they are now firmly established in our cosmic inventory.
Figure 1. John Wheeler (1911–2008). (Source: Wikipedia Commons.)
Figure 2. The Reverend John Michell (1724–1793). (Source: courtesy of go51johnmitchell.weebly.com/biography.html.)
James Clerk Maxwell Foundation
This article is reprinted with permission of the James Clerk Maxwell Foundation (JCMF), which is dedicated to the life and history of Clerk Maxwell. A wealth of information is available at http://www.clerkmaxwellfoundation.org/. In addition, the JCMF owns and maintains an extensive collection of Maxwell material at his birthplace, 14 India Street, Edinburgh, Scotland. Visitors are most welcome once the travel situation returns to normal. This article was arranged by David Forfar and James Rautio, both trustees of the JCMF.
In the late 1700s, natural philosophers were debating whether the nature of light was a particle or a wave. When considering light as a wave. it was difficult to envisage how light could feel the force of gravity. However, if light was made up of particles, it was easier to imagine how gravity might affect particles in the same way that gravity dictates the motion of the planets or of a “Newtonian” apple falling from a tree.
The discovery by Ole Rømer (Figure 3) that light travels at a finite speed led to the notion that gravity could potentially slow down light. John Michell put forward the idea of the possible existence of stars that had a gravitational pull so great that light itself would be slowed down to the extent that it would not even be able to be emitted. The celebrated mathematician Pierre-Simon Laplace (Figure 4) independently made the same prediction as Michell around a similar time. Michell further proposed that these dark stars might be numerous across the night sky but, since they emitted no light, their positions would appear to correspond to apparently empty regions of space.
Figure 3. Ole Rømer (1644–1710). (Source: Wikipedia Commons.)
Figure 4. Pierre-Simon Laplace, (1749–1827), called the French Newton. (Source: Wikipedia Commons.)
Following this initial suggestion of a black hole by Michell and Laplace, the concept was not picked up by scientists at the time. It seemed possible to explain all the properties of light using the wave description, and so the particle theory for light fell out of fashion and the idea of dark stars was probably lost as a result. Although it seemed plausible that gravity could impact light, Newtonian physics was not able to explain it.
This required Einstein’s (Figure 5) theory of general relativity, put forward in 1915, which described cosmic bodies living within the fabric of a curved space and time, such that the planets, stars, and galaxies tell space and time how to curve, which dictates how objects then move through space.
Figure 5. Albert Einstein (1879–1955), portrait after receiving the 1921 Nobel Prize in Physics.
The astronomer Karl Schwarzschild (Figure 6) used Einstein’s equations to show that if matter was compressed to a point, which is now referred to as a singularity, nothing would be able to escape the region of space around it. The extent of this region is known as the event horizon and defines the region of space where it is no longer possible to observe anything that is going on inside this region.
Figure 6. Karl Schwarzschild (1873–1916). (Source: Wikipedia Commons.)
A star begins its life as a huge ball of hydrogen gas. As the gravitational pull squeezes the gas closer together, it heats up until a nuclear fusion reaction begins in the core, causing the star to start shining. This process converts the hydrogen into helium and continues until the hydrogen in the core is almost depleted. The core of the star then begins to contract and heats up further, causing the helium to burn to carbon. The radiation pressure generated by the nuclear fusion reaction inside the star causes it to expand until it balances the gravitation pull holding the star together. This process of contraction and expansion is repeated while heavier and heavier elements are created in the core of the star. The evolution and eventual fate of the star is determined by how much mass the star contains and, for the most massive stars, this process will continue until the element iron is formed. No heavier elements can be produced beyond iron, as the nuclear burning of iron does not produce enough energy for the process to continue.
Once a star has run out of fuel, it begins to collapse under gravity. From our understanding of subatomic physics, we know that particles can be squeezed together only so much. Thus, when a star starts to contract at the end of its life, this contraction will, at some point, stop as the outward pressure from the particles counteracts the inward gravitational pull. This is how a “white dwarf star” or a “neutron star” is formed and is the fate of stars that have a mass of around three times that of our Sun.
Subrahmanyan Chandrasekhar (Figure 7), who went on to win a Nobel Prize for physics, questioned what would happen if a star was more massive than this. What he found was that the pressure from the already compressed particles would not be sufficient to support the star against its own gravity. At the time, this idea seemed completely off the wall.
Figure 7. Subrahmanyan Chandrasekhar (1910 –1995). (Source: Wikipedia Commons.)
The American scientist, Robert Oppenheimer (Figure 8)—famous for leading the Manhattan atomic bomb project in World War II—investigated this further and in 1939 showed that as the gravitational pull of a star increases, the path on which light travels becomes so distorted that nothing can finally escape, not even light. This region of space from which light cannot escape is now known as a black hole.
Figure 8. Robert Oppenheimer (1904–1967). (Source: Wikipedia Commons.)
The event horizon, which defines the edge of this region, is the point of no return; any object that is traveling toward this black hole will not be able to escape once it has crossed over into this region. As an object approaches the event horizon, the end of the object that is nearer to the black hole feels a stronger gravitational force than the other end. As a result, the object is pulled apart or “spaghettified.”
In the late 1960s, Stephen Hawking (Figure 9) and Roger Penrose (Figure 10) showed, from considerations of general relativity, that within the black hole there must be a singularity of infinite density and curvature (of space and time). At this point, the laws of science break down. Observers outside the black hole would, however, be oblivious to this as they would not be able to see beyond the event horizon. This event horizon essentially acts as a cloak of invisibility around the singularity.
Figure 9. Stephen Hawking (1942–2018). (Source: Wikipedia Commons.)
Figure 10. Sir Roger Penrose (born 1931) holding his Nobel Prize. (Source: Wikipedia Commons.)
Another prediction from general relativity is that, as cosmic bodies move through space and time, they send out ripples or “gravitational waves” that carry energy away from the object. For example, as planets orbit around the Sun in our solar system, they send out gravitational waves. As a result, their orbits are ever so slightly reduced due to the loss of energy. This effect is so small that fortunately we do not have to worry! However, a gradually reducing orbit has been seen in pairs of stars that are orbiting each other and, as a result, spiral in toward one another.
Given that only a stellar mass of a few tens of times that of the Sun is required to form a black hole, it was not clear whether other stellar properties made a difference to the black hole that finally resulted. Werner Israel (Figure 11) showed that, according to general relativity, for a nonrotating black hole, only the mass of the star that was present beforehand mattered. All nonrotating black holes were shown to be spherical in shape and their size determined by their mass alone; all of the other characteristics of the star were lost once it became a black hole.
Figure 11. Werner Israel (1931–2022). (Source: Courtesy of researchgate.com.)
This result was the solution to Einstein’s equations that Karl Schwarzschild had found decades earlier. A star need not be perfectly spherical to form a black hole as the gravitational waves emitted when the star collapses would make it spherical in its final black hole state.
For the case where the initial star is rotating, Roy Kerr (Figure 12) discovered solutions to Einstein’s equations which showed that, for rotating black holes, the final black hole rotates at a constant rate, and that their size and shape is determined by their mass and rate of rotation. Rotation means that the black hole is no longer perfectly spherical and bulges around its equator; the faster a black hole rotates, the bigger the bulge becomes. These two scenarios define the two types of black hole: a Schwarzschild black hole, which is nonrotating, and a Kerr black hole, which rotates.
Figure 12. Roy Kerr (born 1934). (Source: Courtesy of ICRA.Net-ISFAHAN Astronomy Meeting.)
Low mass black holes could intriguingly also exist (because they would be well below the mass limit required for stellar mass black holes to be formed). These would have a mass of as little as that of a planet. This type of black hole could form if matter were compacted to an incredibly high density due to large external pressure. Such high temperatures and high-pressure conditions existed in the very early universe, and so these black holes are referred to as primordial black holes. Being able to find these primordial black holes could inform astronomers about conditions just after the Big Bang.
By the late 1960s, the mathematical description and theoretical prediction for the existence of black holes was well established; however, there were no observational data to support this. The question was: How could this evidence be collected if black holes do not emit light directly? The key was recognized back in the 1700s, in John Michell’s original work, where he noted that a black hole (his dark star) would still exert a gravitational force on nearby objects. Pairs of stars orbiting each other, referred to as binary systems, that were locked together by gravity had been regularly observed. Single stars that appeared to be orbiting around some unseen object had also been observed, hinting at the presence of a black hole (the unseen object). This was not concrete evidence however, as the unseen object might not be a black hole, just a very faint star.
In a binary system, if the two objects are close enough to each other, the outer atmosphere of one or both stars can be gravitationally distorted and, in some instances, material can be exchanged from one to another (Figure 13). Considering the case of a black hole (or other compact object like a neutron star or a white dwarf) in a binary system with a star, gas from the star can fall onto the black hole, releasing gravitational potential energy by emitting X-rays. As the material is transferred from the star, it forms into an accretion disk around the black hole. Friction inside the disk causes it to heat up, with the inner region closest to the black hole being heated more than the outer parts. As the material falls toward the black hole and loses gravitational potential energy, part of this energy is released by jets of particles that are directed perpendicular to the accretion disk.
Figure 13. Artist’s impression of a stellar-mass black hole (on the left) accreting material from its companion star as they orbit one another in a binary system. Credit: ESO/L. Calçada/M. Kornmesser.
The galactic X-ray source, known as Cygnus X-1, was discovered in 1964 and was the first observation of a black hole–star binary system. Since X-rays cannot penetrate through the Earth’s atmosphere, early observations of X-rays from space were made using suborbital rockets. Nowadays, astronomers have many space-based X-ray telescopes. By measuring the orbit of the star, astronomers were able to conclude that the object the star was circling must be a black hole as nothing else would be massive enough. Since the discovery of Cygnus X-1, there have been several other similar systems found within our galaxies providing more support that black holes do exist.
Similar observations have been made for the case of supermassive black holes, which are known as quasars. These are extremely luminous objects that were first detected from observations made with radio telescopes. When they were first discovered, there was a great mystery as to what could possibly be producing this emission since they appeared so bright and yet so far away. It has since been concluded that only a supermassive black hole could be the source of these observations. The mechanism is like the above description of X-ray emission from stellar black holes, with material falling in toward the black hole, creating an accretion disk around the black hole.
As the matter spirals in, the black hole rotates in the same direction, which creates a magnetic field, similar in form to the magnetic field around the Earth. As this material gets closer to the black hole, the energy contained within the particles increases and they are then ejected out along the axis of rotation by the magnetic field, creating jets of high-energy particles. These jets have now been seen for many galaxies.
It is still not clear, however, how supermassive black holes, which have a mass of millions to billions of times that of our Sun, are formed. Some have suggested that the collapse of massive clouds of gas during the formation of a galaxy could produce a supermassive black hole or, alternatively, that stellar mass black holes could accrete so much matter that they grow to become supermassive black holes
A further possibility is that black holes, which are sufficiently close to one another, merge to form a supermassive black hole. These are still open questions and an active area of research.
One of the most exciting developments in recent times was the first ever photograph of a black hole in 2019. The black hole was at the center of a relatively nearby galaxy called M87 (Figure 14). It was a historic first for astronomers that was only made possible due to the advanced technology used along with modern computational facilities. It was accomplished by using a network of telescopes which together form the Event Horizon Telescope (EHT) (see “The Event Horizon Telescope Collaboration”).
Figure 14. The first image of a black hole using data collected by the EHT from 2017 to 2019. Credit: EHT Collaboration.
The Event Horizon Telescope Collaboration
The EHT is an international collaboration to capture images of black holes/quasars. The Collaboration has been formed to continue the steady long-term progress of improving the capability of very long baseline interferometry (VLBI) at ever shorter (submillimeter) wavelengths.
VLBI is a technique to measure the time difference between the arrival, at two Earth-based antennas, of a radio wavefront emitted by a distant black hole/quasar, thereby enabling phase coherence (between the different telescopes) to be maintained and data to be sensibly merged. Using this technique, radio telescopes all over the world effectively observe the same source at the same time at the same frequency. This is achieved by linking together radio dishes across the globe to create an Earth-sized interferometer. Thus, many independent radio antennas, separated by hundreds or thousands of kilometers, are arranged to act as one array with an effective aperture of the diameter of the entire Earth. The atomic clocks which are used have a timing accuracy of a few billionths of a second (light travels about 30 cms in a billionth of a second). The frequency stability of these clocks is about one part in a million billion.
The EHT array made observations at a wavelength of m = 1.3 mm (230 GHz). For the EHT, the letter D (see below) is broadly the diameter of the Earth (about 13,000 km), giving an effective angular resolution of about 25 microarc-seconds and with a much higher bandwidth than a single telescope (the angular resolution of a telescope is the angle between close objects that can be seen clearly to be separate and is measured as m/D radians). For better resolution, m/D is required to be as small as possible, so future developments require submillimeter wavelengths. The required surface of each telescope’s parabolic dish is required to be almost perfectly parabolic, with a tolerance of within m/10 (where m = 1.3 mm is the current wavelength of the EHT observations).
Future EHT effort includes deployment of submillimeter dual polarization receivers at a wavelength shorter than 1 mm (230–450 GHz) and highly stable frequency standards.
In April of 2019, the EHT enabled the first supermassive black hole to be photographed. This was M87* in the center of the Messier 87 galaxy (Figure 14). In May of 2022, the EHT photographed Sagittarius A* (Figure 18) as being the black hole at the center of our own galaxy, the Milky Way. M87* is some 55 million light-years from Earth. M87* is considerably more massive than Sagittarius A*, which is only 27 thousand light-years away from Earth.
In both cases, the size of the emission regions matched that of the predicted silhouettes caused by the black hole after allowing for the gravitational lensing of the light that reaches us. The addition of key millimeter and submillimeter wavelength facilities (at high altitude sites) has now opened the possibility of sensing the dynamic evolution of the accretion of incoming matter caused by the immense gravitational pull of the black hole.
By linking together telescopes in widely distant places of the Earth using novel systems, the EHT creates a fundamentally new instrument with angular resolving power that is the highest possible when observing from the surface of the Earth.
As early as the 1930s however, a source of radio emission was discovered in the constellation of Sagittarius close to where the center of the Milky Way was believed to be; this radio source became known as Sagittarius A (Figure 15). Later observations in the 1980s found that this was a complex radio source consisting of several components, including a very compact source that was called Sagittarius A*.
Figure 15. The center of the Milky Way. This image is made from observations (in blue) of X-rays using the Chansra Telescope and infrared data from the Hubble Space Telescope (shown in purple). The inset shows the X-ray emission from Sagittarius A*. Credit: X-ray: NASA/UMass/D.Wang et al., IR: NASA/STScI.
Stars and gas close to the center of galaxies have been observed to have high orbital velocities, which can most easily be explained by a massive object at the center that is creating a strong gravitational field close by. Direct evidence for this being a supermassive black hole was inferred from looking at how material near the center of galaxy is orbiting.
Andrea Ghez (Figure 16) and Reinhard Genzel (Figure 17) were awarded the Nobel Prize for physics in 2020 for their work on showing that Sagittarius A* is the supermassive black hole at the center of our own galaxy, the Milky Way. It is about four million times the mass of the Sun. This black hole has been recently photographed for the first time (Figure 18). It is believed that most galaxies have a supermassive black hole at their center.
Figure 16. Andrea Ghez (born 1965), with her Nobel Prize. (Source: Wikipedia Commons.)
Figure 17. Reindard Genzel (born 1952). (Source: Wikipedia Commons.)
Figure 18. Sagittarius A*, the black hole at the center of our galaxy. It is the second image ever to be taken of a black hole. Credit: EHT Collaboration.
In the 1970s Stephen Hawking conjectured that black holes can radiate energy. This concept is now known as Hawking radiation. The concept behind Hawking radiation is that empty space is not empty of energy after all but contains what is called the vacuum energy. Although, in a vacuum, there may be no particles present, there may still be gravitational and electromagnetic fields with their own energy. From Heisenberg’s uncertainty principle, there are quantum fluctuations in these fields. These fields can generate pairs of virtual particles, which appear together before annihilating each other, effectively zipping in and out of existence. These virtual particles cannot be detected with a particle detector in the same way as real particles; however, their existence can only be inferred from indirect effects, such as changes in the energy of electron orbits in atoms.
Virtual particles are created in particle/antiparticle pairs, such that one particle has positive energy and the other has negative energy (in relation to the vacuum energy) since energy cannot be created out of nothing. Normally, these pairs of particles would rapidly annihilate each other. Close to a black hole though, it becomes possible that one of the negative energy particles crosses the event horizon (thus reducing the energy and mass of the black hole), while the remaining positive energy particle might travel away from the black hole and thus be emitted from the black hole. This emission is the Hawking radiation. However, the timescale for a stellar mass black hole to evaporate completely is expected to be much longer than the age of the universe.
Primordial black holes, on the other hand, have a lot less mass than stellar black holes. As such, they have much smaller evaporation timescales and therefore it is possible that the smallest black holes could have already radiated themselves away through Hawking radiation. The primordial black holes with a slightly larger mass will not have had enough time to evaporate completely and could still be emitting radiation through X-rays and gamma rays. It is possible then to find these black holes from flashes of gamma rays during the final stages of their existence. The astonishing concept by Hawking is that black holes do not live forever and, while a black hole may have appeared to be the full stop at the end of a star’s life, it may continue its own slow evolution and eventual demise.
Pairs of black holes, which orbit in a binary system, have been shown to occur, with the Laser Interferometer Gravitational-Wave Observatory being the first to measure the case of two black holes merging. These black holes were estimated to have masses around 36 and 29 times the mass of the sun.
The merging event begins with the two black holes spiraling in toward each other. This initial phase takes a long time and during the process very weak gravitational waves are emitted. As the distance between the black holes becomes ever smaller, the speed at which they orbit increases, which, in its turn, increases gravitational wave emission. Eventually, they get close enough that they can merge; this is when the emission of gravitational waves is at its highest. Once the merger has occurred, a single black hole is left that will then “ringdown,” by emitting further gravitational waves (Figure 19).
Figure 19. Diagram showing how the emission of gravitational waves correlates with the merging process. The purple line shows the strength of the gravitational waves as time goes by and the black holes get closer together. This peaks when they merge and then is rapidly damped down. Credit: https://astrobites.org/2018/03/08/recoil-detectives-searching-for-black-hole-kicks-using-gravitational-waves/.
In the case of the first merger detected, a black hole that was around 62 times the mass of the Sun was created by the merging event. The sum of the two masses of the original black holes was 65 times the mass of the Sun so that three solar masses were lost immediately as gravitational radiation. This measurement was the first-time gravitational waves were detected, providing further support for Einstein’s theory of general relativity.
Current questions include, for example: How do black holes impact the evolution of the galaxy they inhabit (this is important for understanding galaxy formation)? We still need to understand the implications of Hawking’s conception of black hole evaporation. Measuring the gamma-ray background in order to study primordial black holes is also an active field of research.
From its beginnings as being only a mathematical concept to black holes becoming powerhouses at the center of galaxies, much has been learned about black holes over the last century. It is now undeniable that they play an important role in our wider understanding of the cosmos.
[1] N. C. Robertson, “An introduction to black holes,” Newsletter of the James Clerk Maxwell Foundation, Edinburgh, Scotland, Summer 2022. [Online] . Available: https://clerkmax wellfoundation.org/Newsletter_2022_Summer_V18.pdf
Digital Object Identifier 10.1109/MMM.2022.3233478