Now, let's do something unwise, and travel past the event horizon of a black hole. Knowing that we'd like to get there without being spaghettified, let's choose a supermassive black hole as our destination so that tidal forces don't rip us apart on our approach. Once we pass through the event horizon, we will be in the strange world of a black hole's interior. Although it is impossible to send information about the inside of the black hole to the universe beyond the event horizon, there are no laws of physics that would prevent us, observers within the event horizon from making scientific discoveries. The first thing that we would notice looking away from the black hole is all of the light emitted by the stars and galaxies outside of the black hole. It definitely isn't black inside a black hole. If we shine a flashlight, we find that no matter what direction we try to aim the light, the rays always end up pointing inward to smaller values of the black hole's radius. Before we examine the peculiarities inside of the event horizon, it's worth pointing out just how strange our universe actually is. We have three spatial dimensions that allow us to move about front to back, left and right, as well as up and down. We also consider time, a dimension even though we can only move forward. Something very peculiar happens to the dimensions of space and time at the event horizon of a black hole. Within the event horizon, the radial coordinate, which measures how far you are from the black hole singularity, switches meaning with the dimension of time. Think about it like this, when we're out and about in the universe, we cannot go backwards in time. But in the interior of a black hole, we can no longer go backwards in space. This may give you a headache, but moving to smaller values of radius is really the same thing as moving towards a time in the future. Escaping the black hole would require that you move to larger values of radius, which is equivalent to going backwards in time. Since you can't go backwards in time, you have no choice but to continue to future times, which is the same thing as moving towards smaller value of radius towards the center of the black hole. This might not make much sense if you are thinking of the black hole as a sphere surrounding the point r equals zero. This is a good enough picture for the region outside of the event horizon, but it is not a good representation of the inside of a black hole. We can make a better picture of a black hole by first thinking about how to represent a star that has the same size for all time. In this diagram, since the star is a sphere, all we show is the size of the star's radius. Time runs upwards in this diagram and to the right, we plot distance from the center of the star. Since the star has the same size for all time, the surface of the star is just a straight vertical line. On this diagram, light rays travel on 45-degree angle lines. Now, let's draw a picture of a star that is a sphere that is collapsing to become smaller in size. We are using the same coordinates on this graph, so the surface of the star is a curve instead of a straight line. As time increases upwards on this graph, the distance between the surface of the star and the center of the star decreases with time. Now, let's take the collapsing star and allow it to form a black hole. In this picture, we have the same surface of the star; they get smaller as time increases. But at one special moment in time, the surface of the star is at the same location as the Schwarzschild radius, Rs. At this moment of time, the event horizon forms and is represented by a straight line drawn at a 45-degree angle. The region below the event horizon is the region outside of the black hole, and the region above the event horizon is the inside of the black hole. The jagged line corresponding to what we thought was a point is actually a time in the future. This is a simplified version of a Penrose diagram, which is a tool scientists use to understand the interiors of black holes. More advanced versions of Penrose diagrams further compactify the dimensions of space to a finite region. Since the radial coordinate r takes on the characteristic of a time coordinate, smaller values of distance from the center correspond to later times. There is no way to avoid the flow of time, so any object that is dropped into the event horizon ends up falling to the center at r equals zero. In this diagram, light rays travel on upward paths at 45 degrees. Light emitted in the region outside of the event horizon can go in two directions, the right, which means escaping from the black hole; or to the left, which means falling into the event horizon. Light that is emitted inside of the event horizon still travels on upward directed 45-degree angled lines. Light that is sent in either left or right hits the jagged r equals zero line. Having a powerful rocket engine won't help you escape. All this can do is slow down the inevitable since your rocket can't travel faster than light. The amount of your own personal proper time that it takes to fall from the event horizon to the center of the black hole depends on the mass of the black hole. A higher mass black hole is larger in size and the fall takes more time. The time it takes to reach the center is characterized by this tidy equation, time to fall equals 15 microseconds times the black hole mass divided by the sun's mass. So for the black hole Cygnus X-1 with a mass that is 15 times larger than our sun's, the equation dictates that you'd have about 0.2 milliseconds to relish in the experience of touring the black hole's interior. This amount of time is about how quickly your eyelids take to blink, so you won't even be able to think about snapping a photo of the scene. We now have another great reason to visit high mass black holes. We can have more time to enjoy the sights. For example, if we were to choose a supermassive black hole that is one billion times the mass of the sun, we'd have around four hours of proper time to fall from the event horizon to the singularity at the center. The center of the black hole at zero radius is location of the singularity. Since this location corresponds to a time in the future, you would not see or experience it until the precise moment of time when you reach it. How would objects behave when they arrive at the singularity? Well, since observers aren't able to report back what happens here, we examine what theoretical models of the interior tell us. No matter how massive the black hole, the equation suggest that all of the mass that has fallen into the black hole accumulates at the center and is squashed into zero volume. They also predict that an observer would feel infinitely strong gravitational and tidal forces from which no known object would survive destruction. At this point, you might be a bit confused about the terminology, so let's unpack the word singularity a bit more. To start, I'll state that physics and mathematics have an unequal relationship. In order for physicists to make predictions about physical processes, we need mathematical equations in order to describe likely outcomes. However, it is possible to write down all sorts of mathematical expressions that don't seem to have any connection to physics at all. Many times in the history of science, mathematicians have come up with equations that don't seem to have anything to do with physics. At only many years later, does some physicist discover that the equations actually describe some physical phenomenon. Mathematical equations that describe physical processes are limited to certain circumstances. Outside of those limits, the equations begin to fail, giving non-physical answers. For an example, consider Newton's equation for the attractive gravitational force between two objects with mass one and two separated by a distance r. Force equals G times mass one times mass two divided by the square of the radius. What happens if we allow the distance r between the two objects to come infinitely close together allowing the masses to occupy the same spot in space. In that case, we would set r in the equation to zero, which would mean that we would be dividing by zero in this equation. Dividing by zero is undefined in mathematics and is normally something that you should avoid doing. In order to make sense of this situation, we provide some physical context. What we should remember is that mass takes up space. So, it is physically impossible for the centers of two masses to have zero separation. Since Newton's equation of gravity fails when r equals zero, we should treat them only as a good description of nature if the distance between the objects is bigger than zero. The result when r equals zero is called a singularity. What this tells us is that at r equals zero, our equations just don't make any sense. This type of situation is one that prompts us as scientists to look for a new explanation and more specifically a new equation. We already learned that Newton's equation of gravity is an approximation to those of Einstein. Does that mean Einstein's description of gravity could help us remove the pesky singularity at the center of black holes? Unfortunately, the answer is no. In fact, Einstein's equations predict a divergence of the gravitational fields. Meaning, the problem of the singularity gets even more troublesome than we would have otherwise predicted using Newton's equation. One shortcoming of Einstein's equations for gravity is that they do not include our modern knowledge of quantum mechanics. Quantum mechanics distinguishes itself by introducing the concept of wave functions to describe the positions of particles. Quantum mechanics governs the behavior of particles at scales where Einstein's equations fail. Einstein's equations for gravity assumed that we know the locations and speeds of particles exactly. However, the Heisenberg uncertainty principle, a foundational concept of quantum mechanics, tells us that there is a limit to how precisely we can determine the location and speed of particles. In order for physicists to understand the behavior of the singularity, we need to combine quantum theory with general relativity, which remains a mystery at present. If we knew how to create such a theory, we would call it quantum gravity. One proposed method is called string theory and is a promising set of equations that might describe quantum gravity. However, scientists have not yet managed to solve these equations or make any useful predictions with them. You dear listeners, can take this up as a challenge, the prize for successfully deriving a theory of quantum gravity could win you a Nobel Prize. Many physicists think that as you fall in towards the black hole singularity, the standard equations of Einstein's gravity describe what happens to you for most of the trip, until the distance or really time between you and the singularity becomes much smaller than the size of an atomic nucleus. The region of spacetime that is close to the singularity requires quantum gravity for accurate predictions. Since we don't understand quantum gravity, we can only speculate. Perhaps, quantum gravity removes the concept of a singularity and could potentially describe the existence of a nice remnant. We really have no way of knowing, since the singularity occurs at a time in the future and it can't affect us as we fall in. Ultimately, our lack of understanding of quantum gravity, doesn't affect our journey to the center of the black hole until the moment when we're about to reach the singularity. As we have alluded to before, the singularity inside of a Schwarzschild black hole is a bit of a pesky mathematical object. The singularity simultaneously exists everywhere at the interior of a black hole but only at a specific moment of time. Given that singularities in our universe are not visible to us as far as we can tell they are all hidden behind event horizons, scientists have conjectured the existence of a principle to hide singularities from view, called the cosmic censorship hypothesis. Einstein's gravitational equations predict many different types of singularities. We'll encounter a new type of black hole singularity shortly, a ring singularity. These other singularities are more like a wall that has a fixed location in space and last for a long time. Suppose you run towards the wall, you can see it in front of you as you approach it and if you don't stop, you'll smash into it. A singularity that is like a wall is called a naked singularity. A naked singularity is problematic since we don't have any way to protect what it might emit. The cosmic censorship conjecture states that in realistic astrophysical situations, naked singularities can't form. In other words, the laws of physics keep singularities cloaked by event horizons. Possibly, only singularities like the Schwarzschild version can exist. The cosmic censorship conjecture is yet unproven but at present, we do not see any evidence for naked singularities existing in nature. Well, with one exception, the Big Bang itself is quite possibly a naked singularity. It's likely that in nature, all singularities are surrounded by event horizons. Which is why I'm excited about direct observational evidence for the event horizon of a black hole.