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Black Holes 2: What are black holes made of?

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.

Karl Schwarzschild [Image: Wikimedia Commons]

But, as if often the case in science, even the smartest of us sometimes don’t see the obvious. In 1915, barely a month after the first presentation of general relativity at the Prussian Academy, a young German soldier named Karl Schwarzschild wrote a letter to Einstein, showing that if you use general relativity to consider a situation which has symmetry, the equations become simple enough to solve directly. Schwarzschild considered the case of a source of gravity that was perfectly spherical, 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 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 simple objects.

Cars are complicated, which is why you see lots of magazines like the one on the left. Black holes are simple, which is why you don’t see magazines like the one on the right. [Image: S. Larson]

What do I mean by simple? Consider for a moment one of wonders of the modern age: the automobile. An average vehicle has maybe 20,000 parts that make it up. If you want to understand all the details about how a vehicle works, or make one yourself, you have to understand everything about all those 20,000 parts. What is each one made of, how is it shaped, where does it go in relation to other parts, does it move or is it held still, what kinds of environment will it encounter? These and many other questions are required to have a complete understanding of a “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 spin, and the amount of electric charge 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.

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 black hole and confront some of its exotic properties.

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

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

We can represent gravitational influence with a figure that shows lines along which an object feels the gravitational force. The number of lines emanating from an object is related to the mass. The strength of gravity you feel is related to how many lines are around you (how many lines cross into the little red circles). Stick Spock, far away, feels weaker gravity than Stick Picard, who is somewhat closer. Stick Geordi, who is very close to the source of gravity, experiences much stronger gravity. [Image: S. Larson]

This transition point is important, especially in terms of astrophysics, because it defines which places in space we can detect signals from (for example, light emitted by atoms which can be seen with telescopes), and which parts of space we cannot. Quite literally, the event horizon is an invisible boundary in space that defines “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 exactly the same thing — we’re using a number (that we call “mass”) to express how much gravitational influence the black hole would have on things that might fly around it in space. 

One way to “measure mass” is to look at how long it takes to complete an orbit of a given size. You can do this around the Sun or around a black hole, and they will give the same answer if they “have the same mass.” Compared to the Sun, the gravity of the black hole is only extremely strong when you are close to the hole, seen here in this figure by comparing how close the lines are near each of the objects. [Image: S. Larson]

If you’re scratching you head, you’re doing okay — this is probably one of the hardest things to wrap your brain around. If the black hole has gravity, doesn’t that mean it “has mass?”  Not necessarily.  Consider trying to get as close to the black hole as you can, without crossing the event horizon. As you get closer and closer to the black hole, all you encounter is empty space. In fact, if you fly right through the event horizon to the inside of the black hole, all you encounter is MORE EMPTY 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 stuff — stars, galaxies, nebulae, comets, asteroids, and planets are all made of 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.

Paths ants take when walking along a flat surface. [Image: S. Larson]

Imagine I show you the paths some ants are walking along, but I’ve gotten some of my Hollywood special effects friends to remove the objects they are walking on, and all you can see is their path.  The only rule is an ant always walks on a straight line, directly where its head is pointing, never turning to its left and never turning towards its right. What do you think the ant paths in the figure above are showing?

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.

If the surface has an interesting shape, the paths ants take walking across it, even though they are walking “in straight lines,” look interesting. One path will tell you the surface is interesting (left), but many paths will reveal what the surface really is (right). In this case, a sphere. [Image: S. Larson]

What is that ant walking on? The path the ant took was straight as far as the ant was concerned, never turning left and never turning right. But eventually the path came back to itself not because of something the ant did, but because of the shape of the surface it was walking on! 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.

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!

If the surface has some exotic shape, the ant paths can have a wide variety of different behaviours, but with enough paths you can understand the surface they are walking on. [Image: S. Larson]

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)

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Feeling Small in a Big Cosmos 01: Vastness

by Shane L. Larson

One of the great pleasures in my life is that I am both a professional as well as an amateur astronomer. I spend my days, like many of us do, behind a computer keyboard, staring at a computer screen. I get to think about things that are cool, like black holes and the death spiral of binary stars, and whether or not we can hear the faint whispers of gravity washing over us from some unimaginably distant cosmic shore.

There is nothing quite like standing out in the dark and seeing the Cosmos with your own eyes. [Grand Tetons, by Royce Bair; http://NightScapePhotos.com/ ]

There is nothing quite like standing out in the dark and seeing the Cosmos with your own eyes. [Grand Tetons, by Royce Bair; http://NightScapePhotos.com/ ]

But when I go home, I like to spend long hours of the night out under the stars, in deep personal communion with the Cosmos. Stand out in your backyard, or in a dark mountain meadow, and look up. The sky is deep and vast, studded by thousands of stars, tantalizing bright and inviting, but inexorably far away. If you’re lucky, you can see the Milky Way striking up from the horizon, soaring overhead into the velvet darkness, holding the sky up over your head. I find it deeply comforting to lose myself in that view, to let the Cosmos envelop me in its embrace; some part of me knows “this is home.”

The deep connectedness we often feel with the Cosmos is tempered by another realization: that we are small in the face of the vastness of the Universe. It is an ephemeral and unsettling feeling that is hard to explain and vocalize, but in the opening scene of Cosmos, Carl Sagan captured it perfectly, writing

“The size and age of the Cosmos are beyond ordinary human
understanding. Lost somewhere between immensity and eternity
is our tiny, planetary home, the Earth.”

Beyond ordinary human understanding. We can quantify the scale and age and makeup of the Cosmos, but most of the numbers we are forced to use are big — crazy big! Well outside the boundaries of our everyday experience. Numbers so far outside our everyday experience that to simply state them is almost meaningless, because when we hear them said aloud, our brains fail to process what we are really saying (or hearing). Saying and hearing the numbers fails to adequately capture what we instinctively know, but can lyrically convey one person to another with words that are poetic, but somehow deeply meaningful: somewhere between immensity and eternity.

Our understanding of the vastness of the Cosmos starts not by looking outward, but rather by looking inward. This photograph is one of the most iconic images of the Space Age, known as “The Blue Marble.” There have been many versions, updated every few years as new and better images become available. It looks, for all the world like a child’s blue, glass marble.

The Blue Marble, 2012. [NASA]

The Blue Marble, 2012. [NASA]

There are very few people who, when presented with this photograph, don’t recognize it as the Earth. But here is something to consider: to actually see the entire Earth at once, as it is presented in this picture, you have to be tens of thousands of kilometers away. In all the history of our species, there have only ever been 24 people who have seen the world this way: the Apollo astronauts who made the voyage to the Moon and back.  The rest of us have only become familiar with this image of our small, fragile world though their words, their memories, their pictures. Since that time, now approaching 50 years in the past, the picture has been updated and refined, not by human eyes, but through the lenses and electronics of robotic emissaries, cast out into the night to make voyages that we humans seldom seriously pursue.

The most common and fastest modes of transportation most of us will ever encounter.

The most common and fastest modes of transportation most of us will ever encounter.

This small, blue world is the starting point for all our voyages into the Cosmos, whether they be on ships adapted to the abyss of space, or on wings of thought, unfettered by physical separations in time and space. One way to think about the size of the Cosmos is to imagine making a voyage of exploration. In the stack of notebooks on my desk is one non-descript composition notebook marked “Destinations.” It contains within its leaves lists and notes of destinations on Earth that, given time and freedom, I would love to visit. Kind of my own personal Atlas Obscura.  Many of those destinations can be reached using an automobile, the transport du juor for most of the modern world. Most of us have been in an automobile, and have traveled regularly at a speed of say 100 kilometers per hour (about 60 miles per hour).  By contrast, many of the other destinations can only be reached using the air travel network that girdles our world, travelling by jet aircraft at about 900 kilometers per hour (about 550 miles per hour). Few of us have had the opportunity to travel faster, in a military jet or by rocket.

British astronomer, Fred Hoyle, once remarked “Space isn’t remote at all. It’s only an hour’s drive away… if your car could go straight upwards!” He’s right — the boundary of the Earth’s life-sustaining atmosphere is not that far over our heads. If our cars could drive straight up, we would be off on an epic, Cosmic road trip unlike any other before. Let’s consider a few interesting mileposts, and what their entries might look like in my Destinations notebook. My roadtrip car of choice: a Yugo.

voyages01

Consider Earth orbit — the first stop on the way to anywhere beyond the Earth. For your spaceworthy Yugo, the journey up will be a few hours, and only 23 minutes at the speeds of a passenger jet. By contrast, it took the space shuttle just under 10 minutes to reach orbit.

The Moon was 4 days away if you travelled on Apollo; to drive your car would take 5.4 months of non-stop driving, and just over 17 days by jet. Here, we begin to get the inkling of why exploring the Cosmos is hard — at the speeds of everyday life, even the closest destinations are far away.

Spacecraft take 6-12 months to reach Mars by rocket. Driving in your car would take more than 106 years — longer than a human lifetime. If you left for Mars in a jet when you entered first grade, you’d make it just in time to have your high school graduation on the Red Planet.

voyages02

Pluto has long been the outermost sentinel of the small neighborhood we call home. The New Horizons spacecraft has taken 9 years to fly there, and as of the time of this writing is less than 2 weeks away from its flyby encounter. If the ancient Egyptians had left for Pluto in a spacefaring Yugo, they still would not have arrived— the voyage by car takes almost 7000 years to complete; the voyage by jet takes 740 years.

Beyond the boundaries of the solar system, voyages by ordinary means can be computed, but they become utterly meaningless in terms of timescales. The center of the Milky Way is 26,000 lightyears away, which would take 31 billion years to reach at the speeds of a passenger jet — more than twice the age of the known Universe. The Andromeda Galaxy, the nearest spiral galaxy to the Milky Way, is 2.5 million lightyears away, but it would take us 3 trillion years to reach via jet.

We can compute these times, we can say these words, but our eyes glaze over and we let the words for the immensity of the Cosmos slip by us with little regard for what they really mean. The size of the Cosmos is beyond ordinary human understanding.

The Hubble Space Telescope. Arguably the most capable and successful telescope ever built by humankind.

The Hubble Space Telescope. Arguably the most capable and successful telescope ever built by humankind.

Despite the fact that we can’t voyage across the Cosmos, we can look. The most capable and accomplished telescope the human race has ever built is the Hubble Space Telescope. In its 25 year lifetime, it has seen farther than any telescope before, with tens of thousands of scientific papers published using its data. One of the most remarkable tasks we set before it was the creation of “deep fields.”

Consider the evening skies, shortly after 9pm in January. The constellation of Orion, the Hunter, lies just to the east of the meridian (an imaginary line, running from due north to due south in the sky). Striking out from his western knee is the long and sinuous constellation of Eridanus, the Great Sky River, that winds and wends its way around a non-descript constellation known as Fornax, the Furnace.

Location of the Hubble Extreme Deep Field, between Eridanus and Fornax.

Location of the Hubble Extreme Deep Field, between Eridanus and Fornax.

Between Fornax and one of the bends of Eridanus there is a small, blank patch of sky. Like many patches of the sky, there is nothing there visible to the naked eye. Even far from the city lights, if you stare into the void there, you will see little. To make a Deep Field, we take Hubble, the most storied telescope in history, and stare at one empty spot in the sky. For many days on end. In the case of this lonely spot on the banks of Eridanus, Hubble stared for 23 days.  The result is one of the most startling and revelatory pictures taken in human history.  It is called the Hubble Extreme Deep Field (XDF; NASA page here).

The Hubble Extreme Deep Field (XDF).

The Hubble Extreme Deep Field (XDF).

As you can see, the blank patch of sky is not so blank after all. Every fleck of light, every smear of something in this picture is a distant galaxy, a remote shoal of stars and planets and gas and dust, and just maybe, other intelligent beings staring up at the sky.  All told, in this single image, there are about 5500 individual galaxies. The faintest are 10 billion times too faint to be seen with the naked eye; it took Hubble, the most powerful telescope we’ve ever built, 23 days to see them.

And what have we learned from this picture of the Cosmos? All told, there may be as many as 500 billion galaxies in the entire known Universe. We know that the Universe is 13.7 billion years old, but the oldest galaxies we’ve seen formed soon after the birth of the Cosmos, about 13.2 billion years ago. Big numbers, huge numbers. Numbers beyond ordinary human understanding.

The Cosmos is ginormous (that’s a technical term). It is easy to be overwhelmed when faced with the enormity of it all. But you should also take heart. One of the most remarkable things about the Cosmos, one of the most remarkable things about our species, is that we can figure it out. Despite the size and vastness we have managed to see and understand remarkable and astonishing things about our home, and are capable of pondering the implications of our existence in the Universe. Next time, we’ll explore some of those discoveries and ponderings.

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This post is the first in a series of three that capture the discussion in a talk I had the great pleasure of giving for Illinois Humanities as part of their Elective Studies series, a program that seeks to mix artists with people far outside their normal community, to stimulate discussion and new ideas for everyone.

Part 1: Vastness (5 July 2015)

Part 2: Discovery (11 July 2015)

Part 3: Proverbs (20 July 2015)

Illinois Humanities taped this talk and you can watch it online;  many thanks to David Thomas for doing the videography!