Apie Visatą. Ketvirtoji dalis

 Dabar tai jau nebėra pasakojimas apie tai, nuo ko viskas prasidėjo, tad ir pavadinimą pakeičiau. Taip, aš vis dar pažadu, kad bus ir lietuviškai. Komentarai labai laukiami – šitą tekstuką rašiau per kelis prisėdimus, taigi galimi visokie tik man vienam suprantami minties šuoliai, kurių įvertinimo iš šalies labai norėčiau :) Ačiū.

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Right. So we learnt about where stars come from, how they live and what happens when they die. Except that the last bit can be told in so much more detail – something that I intend to do in the next two or three chapters. This chapter will deal with possibly the most fascinating and mind-boggling objects in the Universe. Yes, you are absolutely correct: today I will tell you about black holes.

First off, here’s some history. When Newton developed his laws of gravity, there have been two theories about the nature of light. One of them, called the corpuscular theory, said that light is composed of tiny particles that zoom around the place, while the other said that light was a wave. Three guesses how that other theory was called. Anyway, some time after Newton, the corpuscular theory gained the upper hand. Now some people were clever enough to combine the thought that light is a stream of particles with Newton’s law of gravity and one of them, a geologist named John Michell, figured that there may be objects so massive that light will fall into them and be unable to escape. This possibility is easy to see today, but back in the 1780s it was a remarkable and somewhat controversial achievement. No wonder that this idea did not attract much following in the scientific community, although a mathematician, astronomer and philosopher (don’t you love how back then, people had several professions and were good in all of them?) Pierre Laplace wrote a little on the subject. However, in the mid-19th century, James Maxwell (and some predecessors) developed the theory of electromagnetism, which brought the wave theory of light back to the top and so the corpuscular theory was forgotten.

It all changed again in the early 20th century, when a young Swiss patent clerk, Albert Einstein, explained the photoelectric effect by using the corpuscular theory. Things started moving rather fast from there, what with the development of quantum mechanics and the notion of wave-particle duality on one hand, and the development of general relativity on the other. It is this latter branch of physics that concerns us right now. In 1915, another young man, this time a soldier on the Russian front in WW1, Karl Schwarzschild, learned of the Einstein equations that describe general relativity. The equations are notoriously difficult – Einstein had trouble defining them and he thought that solutions may be extremely difficult to find. Not to young Schwarzschild, who solved the equations in less than a year. In his free time. While fighting the Russians. In the trenches. Yes, he was just that awesome. In any case, in 1916, the first solution to the Einstein Field Equations was developed, and general relativity could start making testable predictions.

One such prediction was quite startling. If one happens to come within a certain distance of a gravitating body (i.e. anything that has mass), while still being outside of that body, one cannot go out. The only way from there is toward the body, finally hitting it. This distance, called the Schwarzschild radius, marks the boundary of the Event horizon of a body. It is a one-sided surface, because you can only cross it from the outside. It is very small – something like a few millimetres for the mass of the Earth and 3 kilometres for the mass of the Sun, but it does exist. You can imagine that this intrigued many scientists and more properties of such objects fitting within their Schwarzschild radii were discovered. Unfortunately, detecting such an object is extremely difficult, because it does not emit nor reflect any light – hence the term “black hole”, although it was coined only some time in the 1960s. The only two ways to detect them are to measure their gravitational effect or the darkening of objects in their background. It should not be surprising that the first detection of a black hole came only in the late 20th century. As a result, for a while black holes were considered either theoretical curiosities or proofs of errors in the formulation of general relativity.

Even though they were only known on paper, people still developed the theory of black holes. In 1930, Subrahmanyan Chandrasekhar showed that massive stars, once they run out of fuel, will not always become white dwarfs but will continue to collapse further. In 1939, Robert Oppenheimer (of the “I am become death the destroyer of worlds” fame) proved that the next stage in gravitational collapse, the neutron star, is also not the final one. Since no one knew of any other particles that could form from collapsing neutrons and stop the collapse, people realised that neutron stars will probably collapse to singularities, i.e. points of zero volume and infinite density, that would be surrounded by event horizons. In 1963, Roy Kerr found another solution to the Field Equations, this time for a rotating black hole. In 1970, James Bardeen developed a sort-of unified theory of black hole properties, the radiation of infalling matter, the possible orbits around a black hole, and similar things. Thus, slowly but surely people figured out how black holes “work”. Of course, there are many questions remaining, and some even question the fact of the existence of black holes. But these questions are not part of the historical overview.

Now that we are done with history, let me tell you some interesting facts about these black holes. First of all, they generally come in two sizes – stellar mass and supermassive. Stellar mass black holes are remnants of very massive (more than 10 solar masses) stars, formed after a supernova explosion. Their mass ranges between ~3 and ~100 solar masses. There have been quite a few of them observed, and one theory states that they might make up a significant amount of the dark matter in the universe (the MACHO, or MAssive Compact Halo Object, theory). One should beware when approaching them, because the tidal forces around such small black holes are huge, and so an observer would be torn apart long before he could enter the event horizon.

Supermassive black holes (SMBHs) are believed to exist in most, if not all, galactic centres. Our Galaxy has one, named Sgr A* (Sagittarius A-star), so do quite a few other galaxies. The mass of these black holes ranges from a few hundred thousand to a hundred million solar masses. The size of the event horizon is nearly as large as the entire Solar system. Consequently, the tidal forces around such black holes are small enough to not even notice that you have crossed the event horizon. No one is sure how these black holes formed. The two main theories are that they either formed in the very early Universe, long before the first stars were born, and later became the cores around which galaxies formed; or they formed when the first stars ended their lives and exploded and grew to their current sizes later by accreting interstellar matter and munching on other stars from time to time.

What about black holes of masses in between the two extremes? Well, there is a class of objects called “Intermediate mass black holes”, but they are, so far, hypothetical. We have no idea why there are no IMBHs observable. There are a few suggestions – they might be simply invisible and their effects obscured; SMBHs may have formed completely differently from stellar-mass ones and intermediate mass is some kind of a “no-go” zone; we may be living in a time period in our Universe’s history that has no IMBHs (remnants of the first stars have already become supermassive, while younger remnants did not have the time to grow beyond stellar mass yet). Whatever the case, this is all speculation at best.

Another interesting property of black holes is that you can actually see them. Well, not them exactly, but it is possible to see objects falling into them. As a particle is captured by the gravity of the black hole, its total energy decreases (gravitational potential energy is negative). The decrease in energy is radiated away and this radiation can be observed. In addition, matter cannot fall into the black hole directly – it has to lose angular momentum as well, and that cannot be simply radiated away. As a result, rings of matter form around black holes (and, to be fair, other objects, such as white dwarfs), which emit a lot of radiation. These rings, called accretion disks, are the main source of luminosity from active galaxies – approximately 10 percent of galaxies, among them quasars, – making them the brightest objects in the known Universe. Slightly ironic how that darkest object gives rise to the brightest, isn’t it?

There is one more theoretically possible way to see black holes. The keyword here is “Hawking radiation”. You may have heard about it, and I can’t explain it in much more detail than any newspaper article would without going through numerous derivations of general relativistic equations. Qualitatively, Hawking radiation is radiation escaping from black holes. This phenomenon may be explained in two ways – from the standpoint of statistical mechanics or from quantum mechanics. Statistically it is important to note that the entropy in the Universe increases as time goes by. Therefore any particle falling into a black hole will increase the latter’s entropy. This entropy is postulated to be related to the surface area of the black hole’s event horizon. As that area may be calculated, so may the entropy, as well as the change in entropy due to capturing a particle. Furthermore, one can calculate the internal energy change of the black hole due to a particle falling in. Then one can use the relationship between energy and entropy to calculate the effective temperature of a black hole. Now as a black hole has temperature, it must radiate as a black body (much like any object that has nonzero temperature radiates – we do, the Sun does, hot iron rods do, etc.) – we have Hawking radiation. It is important to note here that this radiation is extremely weak, and the temperature of stellar-mass and larger black holes is smaller than that of the cosmic microwave background radiation. This means that such black holes currently grow by capturing background radiation quicker than they lose mass due to radiation. However in several billion years, the process will gradually reverse, with first the stellar-mass black holes, and later even SMBHs, evaporating.

The quantum mechanical explanation of black hole radiation is as follows. The vacuum of space has a certain nonzero energy. This energy level fluctuates very slightly, and some fluctuations may be large enough to cause spontaneous production of particles. These particles annihilate just as quickly, so all the various conservation laws are not violated in the long run. But in this short period when the two particles exist, one of them may be captured by a black hole. If this happens, the other particle has nothing to annihilate with and thus may escape from the black hole, again causing radiation. This concept is rather difficult to understand, and I don’t think I explained in sufficiently well, but trust me that there is a possible explanation of Hawking radiation stemming from quantum mechanics.

And the final interesting property that I will talk about, however briefly, is wormholes. Once again, this subject lies on the fringes of modern science and borders science fiction; therefore there is little of it taught in general undergraduate courses and I can only give a very general overview. You may have seen an explanation of how matter curves space by a two-dimensional analogy: a stretched net with balls placed on it. Each ball pushes the net downwards, creating a well around it. This analogy works quite well, and black holes in such a picture are bottomless wells. Knowing this, it is only natural to ask what is at the bottom of this well. Alright, it may not be too natural to ask such a question, but that’s what we physicists do. And the surprising result is that there just may be an end to most such wells. Again, this is only a theoretical assumption, but let me explain. The event horizon of a black hole is sometimes called a “coordinate singularity”. This is because in the so-called Schwarzschild coordinate system, which is the closest we can get to “normal” (that is, Euclidean) coordinates in curved spacetime, the radial coordinate starts acting funny at that distance from the gravitating object. It appears that objects trying to move to the event horizon would take infinitely long to do so. But they don’t, so there is something wrong with the coordinates. This prompted scientists to look for other coordinate systems in which the event horizon would not be something extraordinary, yet still retain its property of being a one-sided surface. It turns out that there are numerous coordinate systems that fit the bill, but the one which is most interesting is called the Kruskal coordinates. In these coordinates, the event horizon is just a line and the singularity at the centre of it is a hyperbola. Sounds strange, but that actually allows for some very interesting and simple observations, as well as providing new mysteries for science to solve. One such mystery is the presence of an “anti-black hole”, or “white hole” and another event horizon for every “normal” black hole. These white holes should be extremely bright and violate all sorts of conservation laws, because objects would come out of them without ever having fallen in.

It may be that these white holes are the “other end” of black holes, maybe in another Universe, maybe somewhere far away in ours. It may be that we will never know. Currently scientists think that “white holes” are just a mathematical artefact of using the Kruskal coordinates, but we have to remember that fifty years ago, even black holes were thought of as mathematical artefacts. Time will tell what the truth is.

At more than four pages, this is probably far more words than you expected. I do hope this is understandable however. Thank you for reading.

Laiqualasse

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