by Shane L. Larson

In modern astrophysics, the study of black holes grows out of general relativity, the modern description of gravity written down by Einstein in 1915. As descriptions of Nature go, general relativity is among one of the most remarkable discoveries humans have ever made.

On the surface, general relativity seems extraordinarily complex and mathematical, and it can be. The governing equations that describe what general relativity explains and predicts about the Cosmos are what scientists call ** non-linear**. Generally this means the equations cannot be solved with simple pen and paper calculations, using algebra skills you learned early in your mathematical training. This was something Einstein recognized early on. He had in fact abandoned the idea that there would ever be “

*simple*” or “

*exact*” solutions to his equations, and started working on “

*” (“*

**weak gravity***linearized*” for the aficionados) cases where the equations of general relativity can be written in ways simple enough to work on.

**, the equations become simple enough to solve directly. Schwarzschild considered the case of a source of gravity that was**

*symmetry***, like a planet or star or other massive body. Today, we’ve named this solution after him, and the most extreme example of what Nature can do with it is called a**

*perfectly spherical***.**

*Schwarzschild black hole*Most of us have heard quite a few weird and exotic things about black holes, much of which defies our common experience and common sense. That exoticness comes from the sophisticated nature of the non-linear equations of general relativity, but also from the fact that the places where the Cosmos creates or harbors black holes are the most extreme environments imaginable, far outside anything you might encounter on Earth, either on a wilderness hike or in a physics laboratory. But the discomfitting ** exoticness** of black holes belies a subtle truth: they are exceedingly

**objects.**

*simple**car*,” so there are books and magazines and entire industries and trades dedicated to motor vehicles.

Unlike automobiles, black holes are *simple*. They are completely characterized by only three numbers: the ** mass**, the

**, and the amount of**

*spin***they have. Black holes that have one or more of these properties are named for the scientists who first wrote down the mathematical descriptions that describe them in the context of General Relativity.**

*electric charge*These three properties are all ones that seem familiar and quite ordinary, because they are used when we talk about most things in astrophysics. Mass, spin, and charge are all quantities that are more or less familiar. However, in the context of black holes what we mean by them is less clear. Consider “*mass*.” What do we mean by the ** mass of a black hole?** To understand this, we have to first be very clear what we mean by

**and confront some of its exotic properties.**

*black hole*Our adopted definition for “black hole” is a very practical one — it’s an object whose gravity is so strong, not even light can escape. As scientific definitions go, I like this precisely because it is very ** practical** — it captures an immutable way to identify what an object is based on a simple observation or experiment you can do, in this case you can test the

**of an object to see if it is, in fact, a black hole or something else.**

*gravity*One of the things you may remember learning about gravity early on in your science classes is that gravity gets stronger as you get closer to an object, and gets weaker as you get farther away from an object. That means if you are ** far away** from a black hole, the gravity you feel from it does not have to be very strong at all! More to the point, if you are far from the black hole and point a laser pointer directly away from the black hole, the laser light goes flying off minding its own business without consequence; the black hole is so far away its gravity has little or no measurable effect. But that it also means is as you get closer and closer to the black hole, the gravity must get stronger until it finally becomes so strong that the laser light cannot get away. That transition point, where gravity is finally strong enough to stop light, is called the “

**.” It is**

*event horizon**NOT*a physical surface — it is simply that place where gravity has gotten strong enough to overcome light.

*event horizon*is an

**in space that defines “**

*invisible boundary**inside*” and “

*outside*” the black hole. It’s kind of like putting a line of tape across the bedroom you shared with your sibling when you were growing up — there’s nothing to indicate where the boundary is when you walk across it, but there are definite sides. On the outside, atoms are free to create light which can move away from the black hole and be seen in telescopes. On the inside, the gravity has passed the tipping point, and light can no longer get out. Atoms can still go about their atomic business and make light, but that light cannot go sailing across the Universe — like everything else on the “inside,” the light is subject to the inexorable pull of the black hole, dragging it deeper into the interior. For this reason, we treat the event horizon as if it is the surface of a black hole, and for all intents and purposes it is — anything that crosses the event horizon disappears and vanishes into the black hole forever. Every black hole has an event horizon — it is what defines them.

The question that set us along this line of reasoning is “What do you mean by ** mass?**” If the black hole has an

*inside*and an

*outside*, then that seems like an impossible question to answer because the mass lives

*inside*the event horizon — how do you know it has mass? That is an eminently reasonable question to ask! It’s an important one to ask because of the way we talk about black holes. In most contexts,

*mass*is a code word that means “

*the amount of stuff that makes up an object*.” For astronomers, a practical way to think about what we mean by mass is it defines “

*how much gravity a black hole creates*.”

To imagine what we mean by that, try to think about how you measure the mass of the Sun. Has anyone ever taken the Sun and plopped it down on a scale at the doctor’s office? No. We’ve measured the mass of the Sun by observing how its gravity has influenced other objects around it. If I look at the orbit of a spaceship or a small asteroid at a known distance from the Sun, the time it takes to complete the orbit tells me how massive the Sun is. We didn’t “measure the mass” of the Sun (how much “stuff it has” in it), we inferred the mass by ** measuring the gravity of the Sun.** When we state the mass of a black hole, we are doing

**the same thing — we’re using a number (that we call “**

*exactly**mass*”) to express how much gravitational influence the black hole would have on things that might fly around it in space.

**.**

*The black hole has gravity but it is comprised entirely of empty space*Wait — what? That’s right, a black hole is completely empty space. It isn’t tangible, there isn’t stuff you can scoop up and collect in a little plastic bag. It is empty space. So what is it? ** It is pure gravity**. Now it seems weird to think about it that way, because you are used to thinking that things in outer space are made of

**— stars, galaxies, nebulae, comets, asteroids, and planets are all made of**

*stuff**stuff*. But black holes are not. You’ve encountered that idea before — if we go dig a big hole in your garden then lean on our shovels to admire our work, we point at a

*big empty space*, full of nothing, and we call it a

*hole*. This is kind of the same idea.

Now you rightfully might be inclined to ask what is making the gravity? After all, in the rest of the Universe, to make gravity you have to have *stuff*. Isn’t that the point in why we have orbits around the Sun? The Sun has *stuff* it is made of, that stuff makes gravity, and gravity is what makes stuff move in orbits. But gravity isn’t a substance that massive objects make and throw out into the Universe — gravity is an effect they have on the Universe around them. Einstein’s great realization is that what you and I think about as a “*force*” of *gravity is really our response to the shape of the Universe around us* (more properly, the shape of “spacetime”), which is forcing us to move in certain ways. A black hole’s “*gravity*” is just a statement of how the black hole has bent spacetime outside of it. Let’s imagine a simple example.

You might have said a “table” or a “piece of paper” or the “ground” or a “wall.” It could be *any* of these things! You can’t tell the difference between them from the paths, only that whatever it is is FLAT. Now consider the ant paths shown below.

**So what was the surface? From a single path, you can’t tell, but if you have multiple ant paths you begin to see what the underlying shape might be, and there are many possibilities that include the first circular ant path we noted above, but in the end we would conclude it was a ball.**

*shape of the surface it was walking on!*Now consider the more complicated collection of paths below. The more paths you have, the more likely it is you can understand the underlying shape of the space. The ants aren’t feeling any force that makes them change directions they are moving. As far as they are concerned they are walking freely in straight lines, and the shape of the surface they walk on determines what that path looks like. The end result shows you the shape of the space, and sometimes it is flat, sometimes it is spherical, and sometimes it looks like a bottle!

So what should you take away from this parable of the ants? You should know that*how something moves*can be understood as

*moving along the shape of something*. Gravity bends the Universe, and how we move can be understood as us moving along the bends, along the warps and weaves, of that bent Universe. When a planet or a star is sitting off by itself in the Universe, it bends spacetime around it, and black holes do the same thing. When we move along an orbit around a black hole, when we “

*feel its gravity pulling us in an orbit*” we are really just moving along the bent Universe around the black hole.

So what’s the difference between how a star bends spacetime and how a black hole bends spacetime? Only how strongly it does so. The Earth bends spacetime pretty strongly — if you try and jump straight up you can’t get away. A rocket has to travel just over 11 kilometers a second (25,000 miles per hour) to get away. A black hole bends spacetime more strongly, so strongly that you’d have to travel faster than the speed of light, or 300,000 kilometers a second (671 MILLION miles per hour) to get away! Exotic, to say the least!

But despite their exotic nature, black holes had to come from ** somewhere**. Next time we’ll talk about how to make black holes in the Cosmos.

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This post is the second in a series about black holes.

Black Holes 01: Imaging the Shadow of Darkness

Black Holes 02: What are black holes made of? (this post)