 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to talk about black holes. Having previously talked about general relativity, we will try to get a little bit of an understanding of what we mean by a black hole and how they might be detected. So what is a black hole? Well, first of all, simple definition is that it is an object where the gravity is strong enough that nothing, even light, is able to escape. These are not a modern consideration. They were actually considered in the 1700s as dark stars, as objects that with the escape velocity was greater than the speed of light. So we knew of escape velocity, and we could imagine compacting an object down small enough, making it smaller, and then smaller. And as the size decreases, the gravitational force would increase, and at some point it would exceed the speed of light, and this would make a dark star that would then be invisible. But we have a better understanding of what they are when we start looking at relativity. So we looked previously at relativity, remember what gravity is. Gravity is a curvature of space-time. So as the object shrinks, the curvature gets larger and larger. And at enough curvature, even light would be bent back. So in our image here, we see a person standing on an object and shining light in it goes out in straight lines in all directions. That's because the gravitational force is minimal. Relative to the speed of light, a light just travels outward. As you imagine that object being compacted down, light rays start to be turned around and pulled back in through the intensely warped space around the compact object. And if you get enough curvature, then all rays would be bent back into the black hole, making it completely dark. Now remember, these rays are not being pulled by a force. We look at, we talk about gravity as being a force for Newton. After Einstein, the gravity is the bending of space and time. And these light rays are following the only paths they can in this very highly distorted space-time around a compact object. So what is a black hole? What kind of features does it have? Well, it's actually not a very complex object. When we look at just the number of features it has, it has what we call an event horizon. Event horizon is not a physical location, it is simply the radius away from the singularity, the central portion of the black hole, where the escape velocity is greater than the speed of light. And that means we can have no knowledge of anything that occurs inside the event horizon. So any events occurring inside, no matter what they are, we have no knowledge of in the outside world. In order to get that, they would have to travel faster than light, which is impossible. The Schwarzschild radius is the mathematical determination of how far away this event horizon is. Note that both of these get larger as the mass increases. So when there's more mass in the central portion, the event horizon, which is given by the Schwarzschild radius, will continue to expand outward. It is a singularity, while the singularity is a theoretical point of infinite density. So right now we know of nothing that would stop the collapse beyond the degenerate neutron pressure. And at the center of the black hole, this would be then a point of infinite density. Now that leads to its own problems. Is there something else that would stop the collapse? While it would still be a black hole, would there be something inside? However, even if we could go inside to find out, we'd never be able to get that information back out. So it is still a theoretical question as to what really happens to that central object. So what is the size of a black hole? How big are they? The size depends on only one thing, the amount of mass contained inside, and that determines what the size of the event horizon and Schwarzschild radius will be. So you could compress any object to a black hole, including Earth, if you could compress it small enough, and in this case down to 1 cm or less, then the Earth would be a black hole. The Sun to a black hole would have an event horizon of about 3 km, and our entire galaxy to a black hole would have an event horizon of about a tenth of a light year. So even something compressed as much as a galaxy with all the mass of a galaxy would still be very small, remember that the nearest stars are over 4 light years away from our Sun. Our black hole's cosmic vacuum cleaners, and this is a common misconception that black holes just suck in anything around them, and that's really not true. The unusual effects of the black hole are only noticed when you get close to the event horizon. If we could, for example, somehow compress the Sun to a black hole of exactly the same mass, if we had some way to compress our Sun down to a black hole, the Earth's orbit would remain completely unchanged. Yes, it would get cold, yes it would get very dark because we depend on the Sun for our energy, however overall the Earth would continue to orbit the black hole exactly as it orbits the Sun. So what properties does a black hole have? Well, really black holes are relatively simple compared to other objects we've studied. They have three properties, and that's it. They have a mass, how much matter is contained there. They have an electrical charge, whether they have a positive or negative charge, and they have an angular momentum or spin. That's it. No composition or anything else, or any of the other things that we've studied. So a black hole could be made up of hydrogen, it could be made up of iron, it could be made up of peanut butter, it doesn't matter. If you put that amount of mass, of whatever, it's all of that identity gets crushed out of existence informing the black hole, and the only properties that remain are these three. Now as I've said theoretically, yes the matter collapses down to a point, or what we call a singularity, where space and time as we understand them no longer exist. And it is questionable if this thing actually exists, does a singularity exist, or is something else happen when the black hole compresses down. We don't know. That is something we simply do not know at this point. Now let's look at traveling into a black hole. What would happen if you wanted to travel toward a black hole, and what would you notice? Well first of all, under general relativity, as one approaches the black hole, the clocks will run more slowly. Now this is what we will see, I should say. This is what we are seeing from outside. So we would see their clocks slow down. So time would seem normal to us, time would seem, for us looking at them, their time would seem to slow down. We will also note a gravitational redshift from their signals getting longer and longer essentially becoming infinite as they reach the event horizon. And in fact to us the astronaut would appear to stop and never progress through the event horizon. However, this is our point of view looking from far away from the black hole. To the astronauts they see just the opposite. They see that our clocks are running super fast as they get closer and closer to the black hole, but they see theirs as running normally. And remember that it is relative to the observer. So everything appears normal and they just zip through and cross into the event horizon. Now what would happen to them as they get close? Well remember what is happening there. Black holes, like other objects, exert a tidal force. So what that means is that the force is on the foot feet of the astronaut assuming they're going in foot first, would be stronger than those on the head. Stretching the astronaut out in what we call spaghettification. So essentially becoming stretched out like a strand of spaghetti. And that would occur with the black hole as you're getting closer and closer to the singularity. And remember we talk about what these differential gravitational forces do. They exert tides on the earth. But they also can rip objects apart if they get too close to a source of strong gravity. Now interestingly this effect is actually less for a larger black hole. You might think it's the opposite. But a small black hole would tear an astronaut apart. But if it's a supermassive black hole, you wouldn't even know it. You could cross the event horizon without even knowing that you did so. Remember that event horizon gets further and further away from the black holes in singularity. So it's quite possible with a really massive black hole that you could cross the point of return and not even know it. Do objects like this actually exist? How can we detect something that we can't see? We cannot see a black hole. Well we have a couple things. We can use gravitational effects on the orbits. So as one object orbits around another it will follow an orbit and if we look at the orbit of the object going around we can use Kepler's third law to determine the mass of the object inside. So we could then determine the mass of this object and find out if it is too massive to be a neutron star. We have examples that have been seen. One of the earliest ones was the system known as Cygnus X1. Cygnus X1 is a binary system. Now after doing the calculations of the orbits we can calculate the orbital period, we can calculate the distance, we can figure out the mass of the entire system. And we know roughly the mass of the star that exists so we can find out that the other star is 15 times the mass of the sun. But it's not visible. So it's not a regular star we would be able to easily identify a 15 solar mass star of a regular type. A white dwarf star can only be 1.4 solar masses. A neutron star may be 3 or 4 solar masses. So this has to be a black hole. That's the only thing that possibly can explain this. Now we also have the Event Horizon Telescope which has recently given us images of a black hole. Well not the black hole itself but the shadow of the black hole Event Horizon. That's how it gets its name. So we can see the material around the black hole but the event horizon is shadowed out. So we can't see material around that. So we've now been able to do images of this for several galaxies to be able to image that central portion around the black hole. So let's go ahead and finish up with our summary. And what we've looked at this time is that a black hole, the definition is an object whose escape velocity is greater than the speed of light. Black holes have only a few properties which include mass. However, that even that large mass does not make the black hole a cosmic vacuum cleaner. And there is evidence for both stellar sized black holes and supermassive black holes. And we will continue when we get onto galaxies especially to look at these very large black holes that exist at the center of galaxies. 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.