BLACK HOLES

Nobody has ever seen one. Einstein did not believe that they existed. And Stephen Hawking dedicated a major part of his life to them. For 100 years, the black holes of the universe have caused disagreement, fascination, and mystification among astrophysic

For all our detailed mathematical theories, there’s still so much we don’t know... but the discoveries keep coming thick and fast.

“Absurd!” That was the reaction of English astronomer and astrophysicist Arthur Eddington in 1935, when he produced some surprising results concerning the gravity of collapsing stars. For some time, Eddington had been working on mathematical calculations concerning what would happen to stars of different sizes when they ran out of fuel. He used equations from the general relativity theory, which Albert Einstein had developed 20 years previously, and Eddingon concluded that the collapse of a star could sometimes produce what we now know as a black hole.

Eddington should have shouted “Eureka!” instead of “Absurd!”, as his calculations were completely correct. And although he could not accept the result himself, many other physicists adopted it. During the following decades, it turned out that neither the relativity theory nor the idea of black holes in the universe were only mathematical speculation, rather they were physical reality. Today, we know that black holes play a central role for the phenomena that we can observe around us, be it in our own galaxy, the Milky Way, or galaxies which are located billions of light years away. And the relativity theory remains our best key to understanding them.

A black hole is an object, in which there is so much mass in a small area that gravity becomes incredibly powerful – so powerful that nothing, not even light, can escape. That is the reason why we call it a black hole. The first physicist to use the expression was John Wheeler from the US in 1967. But the idea of gravity being able to restrain the light is much older. In the 1780s, 150 years before Eddington’s sceptical exclamation, the first scientists began to work on the idea. One of them was John Michell. Like many other natural scientists of the time, he was a theologist, and in his parish in Thornhill, England, he was both a priest and carried out scientific studies.

Priest developed the idea of black holes

John Michell rode on the wave of mathematical thinking, which Isaac Newton had initiated 100 years previously with his law of gravity, which explained that the forces that make the planets orbit the Sun were the same forces that made his famous apple fall to the ground.

In Michell’s era, light was commonly considered to be particles with mass just like other particles, and that made him wonder what actually happened to the light, when it was emitted by a star. If the star was big enough, gravity would affect the light particles, slowing them down. And if the star was even bigger, they would be unable to escape. Michell named such an object a “dark star”, and he believed that there had to be lots of huge stars that we just could not see, because the light could not escape them. The idea was not bad, and in several ways, Michell’s ideas are much like the present ideas of black holes, although he lacked knowledge. First of all, he assumed that light has a mass, which gravity can affect. Today, we know that light does not have mass. Secondly, Michell did not know that stars of the size that he imagined are too unstable to exist. Now, we now that they would collapse and result in a black hole. Thirdly, Michell lacked a deeper understanding of how gravity works. Thanks to Einstein’s general relativity theory, we now have a fundamentally different view of the interrelation between mass, space, time, and light.

Einstein developed a new formula

Einstein’s theory includes field equations, which describe space in a very different way than the one in which we normally experience it. In our everyday lives, we sense the world around us in three physical dimensions, but in Einstein’s universe, time is included as a fourth dimension, so we get a 4D entity known as space-time. It is very difficult to imagine a 4D space, and so, spacetime is usually illustrated by boiling the four dimensions down to two, so visually, we get a 2D plate or canvas. Any object with mass affects spacetime, so it is deformed. We can illustrate it by the object weighing down the canvas to produce an indentation. In short, there is the following close connection between mass and spacetime: • Mass affects spacetime and tells it how to bend. • Spacetime affects mass and tells it how to move. If we use our own Earth as an example, we can imagine that its mass produces a bowl-shaped indentation in spacetime, and it is this indentation that illustrates the gravitational field. The Moon orbits Earth, because it “rolls” about the edge of the indentation. The heavier an object, the deeper the bowl or indentation around the object.

In Einstein’s field equations, physicists can insert different sizes and observe their effect on spacetime. If they choose a very small object with a very large mass, the bend of spacetime is so powerful that the object produces a deep well around it – a gravity well. If the very heavy object is even smaller, so it has practically no spatial extent, something even wilder happens. The gravity well becomes so deep that Newton’s classical law of gravity no longer applies. The centre of a gravity well, which is infinitely deep, is known as a singularity, and that is exactly what the situation is like in a black hole.

The fact that it can even happen was realized for the first time by German physicist Karl Schwarzchild. Already in 1915 – the same year in which Einstein published his general relativity theory – Schwarzchild studied field equations and found solutions that led to singularities. For decades, Schwarzschild’s results were considered a mathematical curiosity, which did not have anything to do with reality. Even Einstein did not believe that they could exist. As late as in 1939, he published a scientific article, in which he reached the following conclusion:

“The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality.”

So, Einstein was sceptical of the supporters of his own

The result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in reality. ALBERT EINSTEIN in a scientific article in 1939

theory. And this was understandable, as singularity induces a long series of almost incalculable consequences.

In a singularity, gravity is so powerful that nothing can escape it, not even light. Although light has no mass, it is still affected by the gravitational field. Light follows the bends of spacetime, and so, it can be captured in the gravity well just like matter that comes too close.

In the same way as a rocket requires a specific speed to escape Earth’s gravitational field (11,000 m/s), light and matter particles require speed to be able to escape the gravity well surrounding a black hole. Physicists talk about the escape velocity. There is, however, an upper limit to the speed of which anything can travel in our universe. Nothing can travel faster than light at a speed of 299,792,458 m/s. If something is so close to singularity that the escape velocity exceeds this cosmic speed limit, it will never be able to escape. Around a black hole, there is hence a clearly defined sphere, from which even light cannot escape. The limit of the sphere is known as the event horizon, and anything that might happen beyond this limit, we will never be able to see. On the other hand, there is plenty to think about right outside the horizon.

Density makes time come to a halt

If we launch a probe towards a black hole, something bizarre will happen. We will see the probe approach the black hole ever faster, until it reaches the event horizon. From this point in time, we will lose any contact with it, and we will not be able to see what happens to it. That is so, because light particles cannot escape the event horizon, so all information about the spacecraft’s destiny is inaccessible to us.

However, it is not only the light that acts oddly. So does time. If the rocket brought a clock, time would pass ever more slowly, as the rocket approached the black hole. That is so, no matter whether it is a mechanical clock, a digital watch, or an atomic clock. Physicists have named the phenomenon time dilation, and it occurs, because the mass of the black hole not only distorts space, rather also spacetime, meaning that time itself is literally dilated. Inside the black hole, time stops completely, and so, a black hole can be understood as a hole in spacetime.

As our space rocket continues beyond the event horizon to be swallowed by the singularity, the rocket’s mass will be added to the mass of the black hole, which becomes slightly heavier. The larger mass means that the event horizon is also slightly larger, and this is the very way in which a black hole grows. The more it swallows, the heavier it becomes, and the larger the area of space, about which we cannot know anything.

All these consequences follow directly from Einstein’s general relativity theory. The concrete examples would probably unfold slightly differently in the real world, which involves other circumstances that play a role close to the event horizon.

The most important factor is the rotation of the black

hole. If a black hole spins, it means a lot to what happens to the area right outside the event horizon. In 1963, mathematician Roy Kerr from New Zealand managed to find an exact solution to Einstein’s field equations for a spinning black hole, and so, we have a faithful picture of the anatomy of a rotationg black hole.

Today, astrophysicists believe that all black holes have spin, which has to do with the way in which they were formed. Black holes can only form, when a large quantity of matter collapses under the influence of its own gravity. This could happen, when a large star has consumed all its fuel. As long as the star keeps up its fusion processes, it produces an outgoing radiant power inside it, which counteracts gravity. But as soon as the star dies out, gravity is given a clear field of action, compressing the matter of the star. The greater the star’s mass, the more powerful the gravity, and the more compact the matter becomes. When our own Sun burns out in about five billion years, gravity will shatter atoms, making the electrons leave their atomic nuclei. The matter will hence become so compact that the Sun ends up as a white dwarf. It is not sufficiently heavy to end up as a black hole. A star that weighs several times our Sun becomes more compact, when it burns out. In such a case, gravity is so powerful that the electrons and atomic nuclei fuse to become neutrons. The result is a neutron star. Even larger stars of more than five times the Sun’s weight could collapse into even more compact objects. In such cases, even the neutrons cannot resist the pressure, and the result is a black hole – just like Eddington calculated in 1935 much to his own surprise.

Spacetime spins

The collapsing star has a built-in rotational motion that dates back to the time when the star was formed from rotating gas clouds. And although the matter is compressed, the rotation is kept up and becomes even faster. This is due to the same laws of physics that apply to a figure skater performing a pirouette. As the figure skater stretches her arms away from her body, the rotation is slow, but as soon as she pulls her arms close to her body, the spin becomes faster.

That is what it is like with black holes. Close to the event horizon, the spin is so forceful that all particles, even light particles, are forced into the rotation. There, nothing can stand still, as it is spacetime itself which spins around the black hole. We can imagine that spacetime’s “canvas” inside the gravity well is forced around the singularity. This region is known as the ergosphere, and it is vital for the phenomena that we can watch unfold around black holes. If we send something in the direction of a spinning black hole, such as an astronaut, we will experience a scenario that is much more dramatic than the figure skater’s pirouette. The gravitational pull will be extremely more powerful for every metre that the astronaut approaches. If he has his legs in front of him, the pull affecting them becomes much more powerful than the one affecting his head. First, his feet and subsequently his legs and the rest of the body are stretched into something similar to spaghetti. At the same time, the rotation in the ergosphere becomes ever faster, as he approaches the event horizon, so his body is forced into a spiral, encircling the black hole like spaghetti around a fork. Finally, the black hole sucks up the spaghetti, but at this point, our astronaut has luckily stopped feeling anything a long time ago.

Fortunately, this is only a hypothesis. In the real world that we can observe around black holes, it is dust, atoms, and elementary particles that are affected in the above way. That is less macabre, but just as spectacular. All the matter that approaches a black hole is forced into the rotation, so a disc –shaped structure appears around the hole. In technical language, it is called an accretion disc. The closer the matter comes to the black hole, the faster it rotates inside the accretion disc.

Spin converts matter into energy

Huge quantities of kinetic energy are at play in the accretion disc, and this has made astro-physicists wonder, whether it might be possible to extract some of the energy and hence use a black hole as a type of engine. Physicist Roger Penrose was the first to introduce the concept in 1971. His idea was that if you sent a quantity of matter towards a rotating black hole in a way which meant that some of the matter was discarded again, it would include more energy than it did from the very beginning. The energy would come from the ergosphere right outside the event horizon, and the process would hence slow down the black hole’s rotation. In principle, this would enable you to harvest huge quantities of energy from black holes.

Penrose’s idea is just a hypothesis, not a practical solution to the present energy crisis, but his ideas have inspired other astrophysicists to take a closer look at the dynamics of the matter which is spinning in the accretion disc close to a black hole.

The matter which is the closest to the hole travels faster than the matter travelling in slightly larger orbits. The difference of speed means that there is friction, which lowers the speed of the innermost matter slightly, increasing the speed of the matter further out. Moreover, thermal energy is generated in the process, which is emitted as radiation.

If the black hole spins very fast, the matter in the innermost part of the ergosphere can become so hot that it emits X-radiation, which corresponds to temperatures of 10 million degrees. We know no other process in the universe, which converts matter into energy this efficiently.

The conversion of mass into energy takes place according to Einstein’s famous equation E = mc2, by which E is energy, m is mass, and c is the speed of light. According to calculations, up to 42 % of the matter close to a black hole can hence be converted into energy. Moreover, the process is the driving force behind one of the most spectacular phenomena which we can observe in the universe: quasars. Quasars are the most powerful, continuous energy discharges that we know of. They emit powerful radiation across the entire electromagnetic spectrum, i.e. from long-wave radio waves over visible light, to short-wave X-radiation. Quasars are produced by large black holes that convert huge quantities

of matter at the centres of galaxies far away from our Milky Way. Over the past decades, astronomers have had better opportunities to study the structures around the quasars thanks to large radio telescopes on Earth and satellites such as Chandra, which make measurements in the X-radiation spectrum. From the region close to a quasar’s black hole, two powerful jets are discharged, which consist of energy-rich plasma, i.e. charged particles that are smaller than atoms. They could travel at speeds up to close to the speed of light and reach thousands of light years into space. The two jets protrude from the innermost edge of the accretion disc, and it happens perpendicularly to the disc in opposite directions. It is the same structure that astronomers can observe in connection with microquasars, which exist much closer to us, i.e. scattered across our own galaxy. Micro-quasars are also powered by black holes, but they are much smaller. The black hole in a microquasar has a mass corresponding to a handful of solar masses, and it is typically formed by a collapsing star. In comparison, a “genuine” quasar can have a black hole with a mass which is hundreds of millions of times larger.

Black holes eat in a nasty manner

Studies of quasars and microquasars change the traditional impression of a black hole as an object that swallows everything around it. Today, astrophysicists believe that only a fraction of the matter which is attracted by a black hole ends up being swallowed. According to some, it is about 10 %, whereas others think it is more and that it probably varies from hole to hole. Scientists agree that a major part of the matter does not manage to get past the event horizon, rather it is ejected from the accretion disc or as plasma by the powerful jets. So even though black holes are gluttons, you could also say that they eat in a nasty manner.

A black hole could be large an still not end up as a quasar. This is true for the black hole that exists at the centre of the Milky Way. By studying the orbits of stars relatively close to the centre of the Milky Way, you can calculate the mass located in the hole. The calculation requires that you know the spectral class of the stars and hence their masses. If you also know the extents of the stars' orbits and their orbital periods, it is quite simple to get a result. Independent groups of scientists have made the exercise several times, so today, we are quite sure that the large black hole at the centre of the Milky Way weighs slightly more than four million times as much as the Sun.

The black hole at the centre of the Milky Way and the black holes that we observe as quasars at the centres of remote galaxies were not formed by collapsing stars. According to astrophysicists, these supermassive black holes were formed at the same time as the galaxies

around them. This means that black holes are not only spectacular phenomena in the present cosmic era, rather they have been a driving force behind the development of the universe as we know it.

Physicists lack lost information

There is a big difference between the activity levels of the black holes at the centres of galaxies. The black hole at the centre of the Milky Way is rather quiet, and it probably “only” attracts a quantity of matter corresponding to about 300 earths a year. We do not know, what happens to the matter that is swallowed by the black hole, as not even light can escape, and light is usually the carrier of all information. So, we cannot know anything about the matter that the black hole originally formed from. The only things that characterize a black hole are its mass and spin.

American physicist John Wheeler expressed it like this: “Black holes have no hair”. The statement is based on the observation that when we are to characterize another human being, his or her hair could reveal something about the person. Its colour and structure might give away his/her age and ethnic group, and the hair style could indicate sex, culture, etc. Black holes keep all information about their origins, contents, and histories hidden to us. The loss of information in black holes is a subject that has preoccupied physicists for decades. The general opinion has been that at the moment that the matter is swallowed by a black hole, all information about it is lost for good. But is this really so? A theory introduced by British physicist Stephen Hawking might open a "window".

The background is to be found in a phenomenon that follows from “Heisenberg’s uncertainty principle”, i.e. even in empty space, in an absolute vacuum, particles can originate from nothing. In popular terms, you can “borrow” enough energy to produce a particle and its antiparticle. The next moment, they will destroy each other again, and the energy loan is paid back. This activity takes place all the time, and we can even measure it. But what if such a pair of virtual particles were produced right by the event horizon of a black hole? And if the one particle were swallowed, and the other one escaped, before they had time to destroy each other. Then we would suddenly have a situation, in which the energy loan cannot be paid back. The area outside the black hole would have become one particle richer and so have been supplied with energy. So in order to get the numbers right, the particle that was swallowed must have supplied the black hole with a corresponding quantity of negative energy. And as mass and energy are connected, as we know it from E = mc2, the net result is that the black hole has been supplied with negative mass.

When we observe the black hole from far away, we will experience that in this way, the black hole emits particles and so is not quite black. The particles will make up what is known as Hawking radiation.

Since 1974, when Stephen Hawking introduced his theory, other physicists have wondered whether the Hawking radiation might carry information about the inside of a black hole and if we could in principle recreate the details of all the matter that has been swallowed over time.

The speculation caused a famous bet. John Preskill of the US believed that Hawking radiation could contain the information, whereas Hawking himself considered it impossible. But in 2004, Hawking had become convinced that Preskill was right, so he admitted defeat and gave Preskill his prize: a baseball encyclopedia.

However, the discussion is far from over, and it will not be any time soon. Hawking radiation from a black hole has not yet been measured , and so, we cannot tell, whether it contains any information.

If Hawking radiation exists, it will also open different perspectives. It would mean that black holes can evaporate and disappear over time. A black hole that is no longer supplied with matter from the outside, would gradually lose mass via Hawking radiation, becoming ever smaller and lighter, finally ending its life with a quiet “pop!”. According to Hawking’s theory, the process will be faster for small black holes than for large ones.

Hawking’s ideas are an excellent example of the challenges of theoretical physics. The theoretical and mathematical possibilities often reach much further than what we can test by means of experiments and observations. A physical theory might be ever so appealing, but later prove to be utterly incorrect, as it is based on the wrong premises. On the other hand, a theory that seems exotic and is contrary to all intuition could prove to be amazingly correct.

Over a period of 100 years, Albert Einstein’s general relativity theory has time and time again proved its worth, not least its prediction of black holes, even though the scientist himself did not believe that they really existed.

Relativity theory under severe pressure

The equations of Einstein’s theory are very "broad", allowing for possibilities that can be difficult to accept. In the 1930s, Einstein and his student Nathan Rosen concluded that spacetime could theoretically bend so much that two areas that had otherwise been very far apart could be linked by a small bridge known as a wormhole. The idea has inspired many science fiction writers to make their main characters cross huge distances in space in a very short time, and so, worm-holes have been the sources of incredible stories.

If wormholes really exist and can be maintained over a long period of time, they will have even more bizarre qualities. Not only would they allow cosmic shortcuts through space, they would also mean that we could travel back in time. We would be able to move about closed time cycles, in which the future is also the past. In 1949, mathematician Kurt Gödel described a universe that contained such time cycles, in which the same events were repeated over and over again in a never-ending cycle. In a closed time cycle, it would also be possible to kill your own grandparents, before they had your parents, and so,

Things can get out of a black hole, both to the outside and, possibly, to another universe. STEPHEN HAWKING in a lecture in 2015

wormholes and time cycles involve all the paradoxes of time travel.

There is nothing in the relativity theory to prevent the existence of wormholes, but that does not necessarily mean that they exist in our universe. Perhaps unknown laws of nature simply do not allow their existence. According to Stephen Hawking, that is how it is, naming it a “chronology protection conjecture”. Typically for Hawking, he also humorously talked about the conjecture as the principle that makes the universe a safe place to be for historians.

This is not to suggest that Hawking was generally dismissive concerning exotic possibilities in the universe – particularly not when it came to ideas of what was going on inside black holes. Like he said in a lecture in 2015:

“Black holes ain't as black as they are painted. They are not the eternal prisons they were once thought. Things can get out of a black hole, both to the outside, and possibly, to another universe. So, if you feel you are in a black hole, don't give up. There's a way out.”

The same is hopefully true for astrophysicists and their efforts to understand the nature of black holes. At this point in time, we have to admit that black holes not only puncture the universe, rather also our knowledge about it. Einstein’s relativity theory is under severe pressure, as scientists try to describe what is going on in the singularity beyond the event horizon.

The black holes represent the biggest and the tiniest things that we can imagine: incredibly powerful gravity in a very small area of space. Right there, in the singularity, the relativity theory encounters quantum mechanics – the two major physics theories that have not yet been united. Astrophysicists would very much like to develop one unified theory about quantum gravity, which can combine them. Until it happens, black holes will remain the greatest mystery of the universe.