Black holes have an inside and an outside separated by a boundary called the event horizon. What is an event horizon? What does it look like, if it looks like anything at all? Let's explore this concept by revisiting what we mean when we talk about the surface of an object like the sun. We often think of the sun, or any other star, as a big ball of gas which has a surface, but it's an oversimplification to say that all the star's gas lies inside this surface. Some of the sun's material is continually escaping from the hot and energetic surface. The solar wind pushes a small amount to the sun's gas, all the way to the outer edges of the solar system. This is the material that generates the auroras here on earth after all. For stars, we generally define the surface, known as the photosphere, to be the outermost layer of the sun. The photosphere is what we see when we look at the sun in visible light. If we try to look deeper inside the sun, the hot gas blocks the light. So, we can't actually see deeper than the photosphere. Beyond the photosphere, there are additional regions of the sun where gas interacts, such as the chromosphere and the corona, but those layers are very faint and difficult to see. As you can imagine, saying exactly where the sun's surface is located, is a matter of scientific definition. Although black holes do not have a surface, scientists have defined a boundary to separate the interior of the black hole from its exterior. A black hole's event horizon is a boundary that separates the black hole's interior which we are unable to see from the outer region. However, unlike stars, the black hole's event horizon is much easier to define because it's impossible for gas or light to escape from the event horizon. We say that the event horizon is the surface or boundary of a black hole, not as a rigid body but as the point of no return for material that has fallen in. Why isn't it possible to have a ball of gas inside of the event horizon? It all comes down to a concept called hydrostatic equilibrium. In module two, we discovered that hydrostatic equilibrium is the balance between gravity and gas pressure in the interior of stars. Gravitational attraction tries to bring all the gas in the star towards the star's center, but gas pressure creates an outward force that prevents further gravitational collapse. When the stars are in balance, the star is stable and can stay the same size for a long time, like our sun. Suppose we take a star and compress it into a smaller volume, overpowering gas pressure at the interior. The matter in the star will be squashed, and feel a stronger gravitational pull towards the center, which requires a larger gas pressure in order to push outwards to balance the star. Is it possible to continue compressing the star into smaller and smaller regions? No. If you compress the star's gas within the star Schwarzschild radius, the gas pressure required to balance gravity becomes infinite. It's not possible to create infinite gas pressure, so gravity wins the battle and the star's gas will have to continue falling inwards. It is impossible for any matter to be at rest inside of the black hole's event horizon. The event horizon can be understood by observing how light rays are bent by the gravitational field of a massive object. We know that if there is no gravity, light travels in straight lines, just like this ball rolling on a flat surface travels in a straight line. Just as the sheet is deformed by the presence of the weight, space-time is deformed by massive objects, like a star or a black hole. When we roll a ball on the curved sheet, it doesn't travel in a straight line, instead, its path is curved towards the central mass. The closer the ball's starting point is to the mass, the more the path of the ball becomes curved. Light is deflected in the same way by the mass of a star or a black hole. If a star and a black hole have the same mass, deflection angle is the same for photons travelling on paths that are the same distance from the object, assuming the light path stays outside of the object. We must remember that a black hole with the same mass as the star is much more dense. If you recall that the sun's radius is 700,000 kilometers, but a black hole with the same mass as the sun has an event horizon radius that is only three kilometers. This means that it's possible to get much closer to the center of a black hole than a star. The radius of a non-rotating black hole is sometimes called the Schwarzschild radius, named after Karl Schwarzschild, the first person to solve Einstein's equations for strong gravitational fields. Einstein's equations were thought to be so difficult that Albert Einstein himself said that nobody would ever be able to solve them. However, only a year after Einstein published the equations, Karl Schwarzschild found the first solution, which happened to describe a non-rotating black hole. What a coincidence that Schwarzschild, whose name means black shield in German, was the first to describe the concept of a black hole. In module four, we explored the equation for Schwarzschild radius, which is two times the mass times G, over c squared. In this equation, Rs is the distance corresponding to Schwarzschild radius, M is the black hole's mass, G is Newton's gravitational constant, and c is the speed of light. For black holes that don't rotate, the event horizon is a sphere with a radius that is simply proportional to the black hole's mass. So, if you double the mass of a black hole, the radius of the sphere doubles, too. If you put numbers in for the sun, you'll find that the Schwarzschild radius is three kilometers. Physicists often simplify key equations by folding terms that occur repeatedly. In this case, the equation for the Schwarzschild radius is simplified so that it is equal to three kilometers, times the black hole's mass divided by the sun's mass. We now have the event horizon radius scaling with a ratio of masses, or in other words, it's dependent on how much more massive black hole is than the sun. This is helpful as it makes the numbers a little easier. If we were to visit Cygnus X-1, which has a mass that is 15 times larger than the sun's mass, the radius of the black hole would be three kilometers times 15, which equals 45. Still pretty small. The supermassive black hole at the center of the Milky Way has a mass that is 4 million times larger than our sun. This means that its event horizon is 12 million kilometers. That might sound like a big distance, but the largest black hole in our galaxy is smaller than the distance between our sun and Mercury. A black hole would need to have a mass that is 50 million times larger than the sun before the event horizon would be as large as the distance between the sun and the earth. Since the event horizons of supermassive black holes are further away from the black hole center, the tidal forces at the event horizon are smaller for black holes with larger masses. As we learned earlier, tidal forces can be pretty hazardous to an astronaut's health. This means that if you get to choose which black hole to visit, you should choose a larger black hole mass. It is estimated that a black hole should be at least one thousand solar masses in order to be safe to visit. Since the radius of a black hole is proportional to its mass, if matter falls into the black hole, the event horizon grows larger. In most cases, this is incredibly small change. However, if two black holes collide, they can merge into one significantly larger black hole. In case you're wondering, Stephen Hawking proved that it's impossible for a black hole to split into multiple black holes. We'll talk more about this in module seven. If we shine a flashlight in the direction of a black hole, the closer the light is aimed towards the black hole, the more curved the light beam will become. As we aim a flashlight closer and closer, we discover that there's a special distance at which light from our flashlight begins traveling in circles around the black hole. This is an area called the photon sphere, which corresponds to a radius that is one and a half times larger than the radius of the event horizon. The photon sphere is similar to the innermost stable circular orbit for particles, except that circular photon orbits are unstable. If a photon becomes trapped within the photon sphere, only a small nudge is enough to kick photons away from the black hole or to send them spiraling inward. Scientists call this collection of circular photon orbits the ring of fire. In this computer simulation, a black hole is surrounded by the purple and red accretion disk. Some of the light emitted by the accretion disk, travels close to the black hole and becomes trapped in circular orbits for a while before escaping. An observer would see these escaping photons forming a bright ring around the black hole. Current telescope technology is on the verge of capturing images of a photon sphere. New telescopes like the Event Horizon Telescope and others in development should be able to capture images or the ring of fire. If we aim our flashlight closer to the black hole than the circular photon orbit, photons emitted from the flashlight will move on plunging orbits that will end up crossing the event horizon. Any light entering the event horizon is unable to escape. If we can image the region outside the event horizon of a black hole, we would see a region with no light emission, that is sometimes called the black hole shadow. What will happen to an astronaut that is far from the black hole? Let's consider a situation in which both an astronaut and a distant observer are equipped with flashlights capable of emitting one pulse of light per second. If they shine these pulsing flashlights at one another while the astronaut falls towards the event horizon, what observations would we expect them to see? We already learned that gravitational time dilation will stretch the time intervals that the faraway observer sees. As the astronaut falls into the event horizon, the time interval between the pulses received by the observer stretch to infinite amounts of time, even though the astronaut may have only spent a few hours falling into the black hole. Since the event horizon is a one-way street in space-time, the astronaut falling towards the black hole will continue receiving signals from a distant observer at exactly the same rate of one pulse per second. The astronaut even continues to receive the signals after crossing the black hole's event horizon. Remember, the event horizon is asymmetric, just like one-way street. Light can enter the black hole, but it can't escape. The in-falling light pulses from the distant observer don't change as they pass through the event horizon to be observed by the astronaut. Just as there is no wall of gas left over from us compressing a star, there's nothing special marking location of the event horizon. This makes a trip to a black hole extremely dangerous. If you manage to survive the tidal forces near a black hole, it is easy to accidentally crossover the event horizon since it seems like an unremarkable location in space when you're traveling through it. So, if you do travel to a black hole, be sure to calculate exactly where the event horizon is before you approach. We know that anything entering a black hole's event horizon cannot escape. Not even light. This means that you can't sneak a look at what's inside and let people outside know what's happening. While you obviously wouldn't risk putting your head into a black hole, if you're sitting inside your rocket orbiting just outside the event horizon, you could lower a camera past the event horizon. However, in order to take a picture of the inside of a black hole, the electrons in the camera would need to travel faster than the speed of light to send any information back up to your spaceship. We expect that the structure holding the camera will be ripped apart, and that the camera would fall inwards before any photos could be taken. Even though we can't, in theory, pass information about the interior of a black hole past the event horizon, we can deduce some of the properties of a black hole's interior. One object theorized to exist by Sir Roger Penrose is called the singularity, an object so foreign to the laws of physics that our understanding of them is incomplete. Singularities are thought to be such dreadfully ugly objects that we think the event horizons themselves are there to shield us from seeing it. This yet unproven conjecture is sometimes called Cosmic Censorship Hypothesis, and we will go into more gory detail in the next section.
