 Greetings and welcome to the introduction to astronomy. In this video we are going to talk about black holes, one of the stranger objects that we will encounter in astronomy that have some very unusual properties about them, and are really also some of the very important objects in that they make up the centers of galaxies. There is a supermassive black hole, many millions times the mass of our sun, at the centers of galaxies. So let's take a look and try to learn a little bit more about black holes. So what is a black hole, first of all? The definition of a black hole is an object with such a strong gravity that nothing even light can escape. Now anything has an escape velocity, there is an escape velocity from the earth, there is an escape velocity from the sun, there is an escape velocity from the solar system, and from a galaxy, and from a star, and from a black hole. Now what this means is that if you are traveling at a speed greater than that, and there are no other forces involved, then you would be able to escape, and if you are traveling at a slower speed then it would not be possible. Now these were actually considered as far back as the 1700s, so we had the concept of a black hole, which was just an object with an escape velocity that was greater than the speed of light, and those were proposed by Laplace and Mitchell, two different astronomers and scientists of the time. So they had come up with the idea long before an understanding of general relativity or anything else that would be needed, but simply based on the fact that if you compressed an object small enough then its escape velocity would increase. So if we look at an object and we make it smaller and smaller and smaller, the size decreases so it's getting smaller as the object here gets smaller and smaller, then the gravitational force at the surface would increase, and then the escape velocity would get larger and larger. So it's easier to escape from this larger object, harder from the smaller one, and maybe impossible from this much tinier object just because of the intensity and how deep the gravitational well is as you compress that material down. So let's continue on here, and what we see is in terms of black holes and looking at them with general relativity, remember general relativity describes gravity as a curving spacetime, so space and time curve, and what happens is the object shrinks, this curvature gets larger and larger and larger. If the curvature is large enough then even light would be bent back in on the black hole. So we can see that in our image here, at an ordinary object if we shine a flashlight out all of the rays are able to escape. They are traveling at greater than the escape velocity and they can easily escape from this object. In this case as we get to compact the object down and it gets denser and denser, then only the light rays going straight away still can escape. Those trying to follow other paths end up getting curved back in on the black hole. So they are unable to escape. Now remember that under Newton, unlike under Newton, there is no force involved here, so there is not a gravitational force pulling on these light rays. It is the light rays following the paths that they can. They follow the only paths that they can in this highly distorted space and time. And as that object compresses down towards a black hole it gets really very, very distorted. So what is a black hole? What is a black hole? What are the parts of a black hole essentially? And black holes are actually relatively simple objects in that they don't have a lot of parts to them. They only have a few things that we can actually know about them. One we talk about is the event horizon. The event horizon is sometimes what we see as or call the surface of the black hole. Not a true surface, there is nothing there. It is just a distance from the center of the black hole and it is the distance at which the escape velocity equals the speed of light. So the escape velocity is equal to C, the speed of light, meaning that inside this nothing can escape. So we know nothing about what is going on inside here. Outside of it, light could still escape barely because it is traveling faster than the escape velocity at that point. But essentially within the event horizon, we can have no knowledge of anything that occurs this close. Now in order to determine the event horizon, we can calculate what's called the Schwarzschild radius. The equation for it is given here and it simply depends on the mass of the object. The mass of the black hole does not depend on anything else. 2G and C, the speed of light squared, are simply constants. So the mass is the only thing that matters here. But it is a way to determine it mathematically and as the mass increases, the radius will get larger and larger. So the Schwarzschild radius will get larger and therefore the event horizon gets larger because the Schwarzschild radius is just a way of measuring the distance from the singularity at the center to the black hole. To the, sorry, for the distance from the singularity at the center to the event horizon. Now the singularity is a theoretical point and that is what is conceived to happen right now. That everything will collapse down. There is nothing that can stop that collapse and eventually it will reach a pin point of infinite density. So it could have been all the material in a star, but it is now collapsed down to just a single point, smaller than the tip of a pin that is compressed there. All the material is compressed down to there. So all the mass is down at the singularity. The nothing else would be left in between. So how big can a black hole get? Well, black holes come in all sorts of sizes. And in fact, if you compress an object down small enough, you can make any object a black hole. It depends only on the amount of mass there. So if we want to make the earth into a black hole, we have to compress the entire earth down to an object less than 1 centimeter in size. So that's all of the earth, all of us, everything on the earth. Compress that down to 1 centimeter and the earth would then be a black hole. If we want to make the sun into a black hole, we'd have to compress it all down to about 3 kilometers, about 2 miles. So very, very much larger, much more mass in the sun than in the earth. If we want to make our galaxy into a black hole, we would have to compress it down to about 1 tenth of a light year. Remember that our galaxy is 100,000 light years across. So we have to compress that all down to something much, much smaller than the distance to the nearest star, which would be about four light years. This would be 1 tenth of a light year. So we're essentially compressing a galaxy down to something not much bigger than a solar system. Now one of the misconceptions about black holes is that there are these great big vacuum cleaners, and they will just swoop up everything anywhere near them. And this is not correct. They are not black. They are not vacuum cleaners. And actually, the unusual effects of a black hole are only noticed close to the event horizon. So at the event horizon, we will then be again to notice some of these, and we can note that there are unusual effects there. If, for example, as an example, if we were to convert the sun to a black hole, somehow compress the sun down to this three kilometers in size and not change the mass, just somehow compress it down, the Earth's orbit would be exactly the same. We would continue to orbit around it with a period of one year, and nothing would actually change there. However, it would get awful cold and awful dark. The Earth would freeze. The atmosphere would freeze down to the Earth. We'd lose all of our source of heat and light. But in terms of the orbit, the Earth's orbit would be completely unchanged, not even the slightest change to it, because of that we are actually a whole 93 million miles away from something that is only really the events that don't really get important to you and get within a couple miles of it. Now, we looked a little bit about some of the radii of a black hole, but how about other properties? What can we know about a black hole? And that can be a very difficult thing to really learn anything about a black hole, because they are, as I've said, very simple properties, very simple objects. They have only three properties. So we talked about things with stars, we can talk about temperatures, and we can talk about compositions, and we can talk about all other things. But black holes have only three properties. They have a mass, how much material it contains. They can have an electrical charge if they have a net positive or negative charge. And they can have angular momentum or spin. That's it. There is nothing else that we can know about a black hole other than these three things. So we only know three things about it that makes them relatively simple objects in terms of being able to understand them. We don't have to worry about the compositions or anything else. And we honestly cannot tell the difference if a black hole were made up of hydrogen, or iron, or uranium, or any other element. We would not be able to tell the difference. Everything else would still be about the same. It only depends on the mass, not what the mass is made of. So in terms of composition, it really does not make any difference. We can ignore the composition. It does not matter what they are made up of. In terms of what we see about a black hole, the electrical charge is also generally not very important if a black hole were to get a significant positive or negative charge. It would then attract ions of the opposite charge because the electromagnetic force is much greater than the gravitational force and it would very quickly neutralize itself. So we don't usually worry much about positive or negative charges within a black hole. But in terms of mass, we will look at that and we can also consider spinning. Now, theoretically, a black hole does collapse down to this singularity. Does this really exist? Well, many astronomers will tell you that the idea of a singularity is questionable. So we don't really know what happens inside the black hole. What happens once we start crushing those neutrons in upon themselves? Yes, it will get smaller and smaller, but will it actually condense down to a point or is there something else that will stop it? It doesn't change it from being a black hole, but it could change our exact understanding there and that's one of the problems is that we don't really understand how general relativity does not work on these kind of scales. It does not work on the quantum scale. So we need looking for theory that would be able to combine general relativity and quantum mechanics to be able to better understand what goes on deeper down inside that black hole. But within it, if you get down to a singularity, things like space and time have no meaning anymore. So even within a black hole, space and time can get so twisted up that it is not what we would normally be used to. In terms of we get used to traveling through space in various directions, we get used to traveling through time in one direction at one speed. And it's possible that within a black hole, you could actually travel through time. However, you are then confined to travel in only one direction and that is towards the potential singularity at the center of the black hole. So perhaps it is a way to travel through time, but since you can't get back out, it doesn't do any good. So now let's imagine a trip into a black hole if we were to actually travel there and if an astronaut were to travel towards a black hole, what would he or she notice? Well, as he approaches the black hole, clocks begin to run more slowly. Remember that the closer you get to a strong gravitational field, the slower clocks will run. And we can notice that even here on Earth with clocks in orbit versus clocks on the Earth's surface and that's a very small gravitational field. So in a black hole, it would become even more extreme and this is what, first of all, I wanna make sure we qualify here. This is what we would notice. So as we watch it, we would see the astronauts' clocks run more slowly. The astronaut would notice no difference. We would notice a gravitational redshift from his signals. As he sends out signals, they would get shifted to longer and longer wavelengths, eventually getting shifted infinitely as he reaches the event horizon. And from our point of view, the astronaut would appear to stop at the event horizon. Time would essentially stop for us, for our perspective, watching him and nothing would happen. To the astronaut, however, everything appears perfectly normal. He would see our clocks as running really, really fast but he would just continue down towards the black hole and then eventually cross the event horizon. Now, what does that mean? Well, as we get close to that black hole, we get a term we know as spaghettification and this is because black holes exert tidal forces and that means as you're looking from the black hole here to the astronauts' feet, this is one distance and if we look from the black hole to the astronauts' head, up here, that is another distance and because the gravitational force depends on the distance, there is a stronger gravitational force on his feet than there is on his head and that means the astronaut would then be stretched by tidal forces. Now, this is what happens here on Earth because of the moon but to a much smaller effect. The moon is able to stretch and pull the Earth a little bit. However, as you get close to a black hole, it could be very extreme and would actually eventually stretch and squeeze the astronaut into a very long, thin, essentially, string of spaghetti. So the force is on the feet, stronger than the force is on the head, which causes this stretching. Now, interestingly, this effect is actually less for a larger black hole. So a smaller black hole, say something with the mass of the sun or 10 or 20 times the mass of the sun would tear our astronaut apart. However, you could cross the event horizon of a supermassive black hole, millions of times the mass of our sun, without even knowing it. So, since we look at this, now what can we say? Do black holes exist? And that is a good question. How do you detect something that you can't see? If we can't see it, how do we go about detecting it? Well, we can look at gravitational effects in orbits and we can then use Kepler's third law to determine the mass. Cygnus X1 pictured here is an example of this. It is a binary system and we can do calculations based on knowing what type of star this is and determining how much mass has to be here based on Kepler's third law. And what we find is that that object there must be 15 times the mass of the sun. Much too large to be a white dwarf, more than 10 times larger than a white dwarf could be and about three times larger than a neutron star could possibly be. So this cannot be a white dwarf, cannot be a neutron star, but it can be and likely is a black hole. So this was one of the earliest detections of inferences that a black hole would exist. Now this isn't the only example. There are others. We can also look at X-ray emissions. So as material spirals into the secretion disk and spirals into the black hole, it gets heated up to millions of degrees and at temperatures of millions of degrees, it will emit X-rays. So X-rays are given off in that emission and that is one way to really be able to measure again the black hole, measure the black hole. We also can have supermassive black holes and these we can talk about when we talk more about galaxies, but these do exist at the center of most, if not all galaxies. And they are also seen through gravitational effects and X-ray emission. So we'll look more about that when we talk about galaxies, but they do exist there as well. So let's finish up here as we do with our summary and what we find is a black hole is simply defined as an object whose escape velocity is greater than the speed of light. Those are the two key things we need for a black hole. It has to have an escape velocity larger than the speed of light. That means that nothing, since nothing can travel faster than light, nothing can escape from the black hole. They have only a few properties. Primarily mass is one of those. That large mass, however, does not make the black hole a cosmic vacuum cleaner. Again, the sun turning into a black hole would have no impact at all on the Earth's orbit. And we have talked about some of the evidence. There is evidence for both stellar-sized black holes and even supermassive black holes those millions of times the mass of our own sun. So that concludes this lecture on black holes. We'll be back again next time for another topic in astronomy. So until then, have a great day, everyone, and I will see you in class.