The Man Who Helped Predict Black Holes, Both Real and Hypothetical

It was cold on the Russian front that day in 1915. The German artillery officer stamped his feet and wrapped his greatcoat around him as he looked at the strange package that had arrived in the battalion mailbox, wrapped in butcher’s paper and tied with string. When he opened the package later in his billet, he was surprised to see that it was an issue of the Prussian Academy of Sciences’ journal containing a paper written by his erstwhile colleague in Berlin, Albert Einstein. This was the famous paper in which Einstein laid out general relativity.

The man was no ordinary artillery officer. Before the start of the First World War Lieutenant Karl Schwarzschild had been Herr Doktor Professor Karl Schwarzschild, the director of the prestigious Potsdam Astrophysical Observatory, one of the most important positions in German science. Because of his age and position he could easily have avoided military service, but like many European men caught up in the nationalistic fever sweeping the continent, he volunteered for the army. He spent the early years of the war working out the effects of wind and temperature on the trajectory of artillery shells, a task that brought him to the Russian front on that fateful day in 1915.

People who had wrestled with Einstein’s equations up to this time had tried to in general solve them for the entire universe. Schwarzschild took a dif­ferent path, one well known to theoretical physicists. Confronted with a complex system that defies analysis, one way to proceed is to look for the simplest possible example of that system in operation. The hope, of course, is that the solution for the simple case will give you a hint about dealing with the more complex one.

Following this path, Schwarzschild decided to look at a system consisting of a single massive body surrounded by empty space. Think of this as an attempt to apply general relativity to a single isolated star. The advantages of this approach are obvious. For one thing, you don’t have to worry about the direction in which you approached the massive body— you can just assume it’s a sphere so that all directions are the same. In addition, by taking this approach you can ignore things like the effects of electric charge and rotation, complications that would have to be dealt with eventually but could be ignored at the start.

With these simplifying conditions, Schwarzschild was able to solve the Einstein equations, laying out simple results that described the warping of space-time by the presence of an isolated mass. His solution had many appealing properties. At large distances from the mass, for example, it gave the same well verified results that Isaac Newton had written down centuries before. It was only as you got close to the mass that things began to get weird.

Schwarzschild approached this weirdness by thinking about the concept of escape velocity. Look at it this way: when you throw a ball up from the surface of the Earth, it can climb to only a certain height before gravity makes it slow down, stop, and fall back down. There is some initial velocity, however, that will be so fast that the earth won’t be able to hold on to the ball. It will just keep traveling upward and leave the planet forever. We call this transitional speed the “escape velocity.” For Earth, it’s about seven miles per second.

As a seasoned artillery officer, Schwarzschild would naturally think of objects traveling near his central mass in terms of escape velocity. Put an object anywhere in space around the central mass, and there will be some outward velocity that will allow it to escape and find refuge in the Newtonian outer reaches of the system. He saw that the closer you got to the central mass, the higher the escape velocity would be.

It was at this point Schwarzschild noticed something strange. If you look at the escape velocity as objects get closer and closer to this central mass, you eventually reach a point at which the escape velocity exceeded the speed of light. Since one of the main results of the theory of relativity is that nothing can travel faster than light, it followed that nothing closer to the central mass than this crucial distance can ever escape to the outside world. That fact defines what we now call the “event horizon”—the distance of closest approach beyond which escape becomes impossible. Though he didn’t know it at the time, Schwarzschild had discovered what would later be called a “black hole.”

We don’t have direct evidence that Schwarzschild and Einstein had known each other in the prewar days, but as prominent members of the Berlin scientific community they would certainly been aware of each other. Schwarzschild sent his results to Einstein with a friendly letter, ending with, “As you see, the war is kindly disposed toward me, allowing me, despite gunfire at decidedly terrestrial distance, to take this walk into your land of ideas.”

Einstein was impressed by Schwarzschild’s work; he said he had had no idea that such a simple solution to his equations was possible. Consequently, he presented the work to the Prussian Academy, in those days standard procedure for publicizing work that someone else had done.

We would love to have been able to close this excursion into history by recounting Schwarzschild’s triumphant return to a position of leadership in the German scientific community. Alas, it was not to be. A few months after Einstein’s announcement, Schwarzschild was diagnosed with a disease known as pemphigus, an autoimmune condition often found among Ashkenazi Jews. He was invalided out of the army and died shortly thereafter in Germany,

Perhaps the most amazing thing about Schwarzschild’s results as far as black holes are concerned is that for almost half a century no one believed that his results could apply to objects in the real world.

The key fact about Schwarzschild’s solution to the Einstein equations is that when an object gets closer than a certain distance from the central mass it can never get back out. This distance is called the Schwarzschild radius, and the spherical surface it defines in space is called the event horizon. The Schwarzschild radius of an object depends on its mass. The higher the mass, the greater the Schwarzschild radius. Put another way, for every object of a given mass, there is a radius defined by the fact that if all of the mass of the object is confined within that radius, that object will become a black hole. The density of mass in a black hole can be extraordinary. To turn Earth into a black hole, for example, the entire mass of the planet would have to be confined within something about the size of a marble.

Once we have established the existence of an event horizon, however, we can start to think about what it would be like to approach a black hole. Suppose you had three spaceships located in deep space, far from the black hole you want to approach. Each of these spaceships is equipped with a device that sends out light signals of a given frequency and another device capable of detecting light of all wavelengths. Two of the spaceships set out side by side toward the black hole, while the third stays in deep space and watches. What will observers on the spaceships see?

To answer this question, we have to go back to one more prediction of general relativity, one involving the interaction between light and gravity. Imagine shining a flashlight straight up from the surface of the earth. One way of thinking about what happens is to say that the light is climbing up from the bottom of a gravitational hole. It takes energy to do this. If we threw a baseball, we know that it would slow down as it climbed up. But light can’t slow down—it must travel at the velocity we’ve called c, so the energy has to come from somewhere else. According to general relativity, as the light climbs up its frequency (and hence its energy), blue light shifts down to red, which shifts down to infrared, and so on. This is called the “gravitational red shift.” It is one of what are called the classic tests of general relativity, which was first seen in the laboratory in 1959 and today is universally used in GPS systems, which involve clocks high above Earth sending signals up and down in Earth’s gravitational field.

Going back to our spaceships, we can think of the light being emitted from each as a clock that is ticking a billion billion times per second. As the twin spaceships descend toward the black hole, they will move faster and faster, and as a result the time dilation will get bigger. This will be interpreted by the distant observer as the clocks on the traveling ships slowing down. As far as this observer is concerned, the clocks on the falling ships will “tick” more and more slowly until, when those ships reach the event horizon, they stop entirely.

On the other hand, the observers in the moving spaceships see their own clocks and the clocks in their companion ship ticking normally. For them there is nothing special about the event horizon—they just sail right on by.

We can carry the spaceship analogy a little farther by asking what happens once they are inside the event horizon. The passengers on the spaceships won’t notice anything in particular when they pass inside their “black hole”: the same laws of physics will apply both inside and outside. There will come a point, though, when the spaceships will reach what is called a singularity at the center of the black hole. It is a point when the familiar rules of physics break down and all hell breaks loose. The existence of the singularity was one of the main reasons physicists refused to accept the reality of black holes in the early and mid-twentieth century.

Black holes showed up in the physics literature early on, though they weren’t called black holes at the time. For a generation of scientists who were used to exploring the heavens with telescopes, black holes posed special problems. We normally detect objects in the heavens either by the light they emit (we see stars this way) or by light they reflect (we do this every time we look at the moon). Neither of these will work for a black hole, because once light passes inside the event horizon it can never come out to enter your telescope.

But that wasn’t the only problem. As we have pointed out, according to Schwarzschild’s solution, every object in the universe has a Schwarzschild radius and could therefore become a black hole, at least in principle. All that has to happen is that all of the mass of that body has to be crammed inside that radius. The problem was that no one could imagine any physical process that could produce that kind of compression. As we have seen, for Earth to fit inside its own event horizon the planet would have to be crushed down until it was about the size of a marble.

The small size of black holes relative to their mass gives rise to an interesting phenomenon that wasn’t noticed by Schwarzschild and his colleagues but has become part of the folklore of black holes. You can understand this phenomenon by recalling that the force of gravity between two bodies increases as the bodies get closer to each other. Cut the distance between the bodies in half and the gravitational force will increase by a factor of four. Cut it to a third and the force increases by a factor of nine, and so on. The closer you can get to the center of a gravitating body, therefore, the greater will be the gravitational force you experience.

When you are on Earth’s surface you are about four thousand miles from the center of the planet, and the force of gravity at that distance is what produces your weight. Were Earth to become a black hole, however, you would be able to stand a fraction of an inch from the center. At this distance, your weight would increase over a million trillion times over what it is now.

This raises an interesting question about what would happen to a human observer who tried to approach a black hole. Obviously the force of gravity on the observer would increase as he or she approached the event horizon. Long before arrival, however, another effect would make itself felt. You can understand this new effect by noting that when you stand on Earth’s surface your feet are closer to the planetary center than your head. This means that the gravitational force on your feet is (infinitesimally) larger than the force on your head. The extra few feet your height adds to Earth’s radius is so small that it can safely be ignored. If Earth became a black hole, however, the force associated with those extra few feet would become huge.

Suppose our hypothetical traveler was approaching the compressed Earth’s event horizon feet first. The difference in gravitational attraction between his or her head and feet can be thought of as a force acting to stretch the observer’s body. As the observer approaches the event horizon, that stretching force would become larger and larger until, eventually, it exceeded the internal forces holding the body together. Most likely the ligaments holding the joints together would snap first, but eventually the difference in gravitational force would become so great that the bones themselves would be pulled apart. This stretching phenomenon has been given the amusing name of “spaghettification.” It can be a hazard for astronauts who get too close to a black hole. Having said this, however, we will argue later that objects approaching a supermassive black hole will not be spaghettified. This is because the supermassive’s radius is large enough to cancel the effect of its large mass.

Assuming the observer has survived the journey though the event horizon, we can use Schwarzschild’s solution to talk about the rest of the journey, even though we can no longer communicate with the inside of a black hole. At the very center of the interior of a black hole, Schwarzschild’s solutions simply blow up, a term physicists use to describe the process by which quantities dealt with in their equations become infinite. Since nothing in nature can actually become infinite, physicists preferred to believe that black holes couldn’t actually exist rather than face the fact that their theories didn’t work. It was an easier way out of the problem than the proposed solutions we’ll talk later.

Once theorists accepted the reality of black holes, they were free to apply their theories to the question of the kinds of black holes that might be out there. Not surprisingly, over the years, many dif­ferent types of black holes have been proposed, some of which have actually been discovered, some of which have not (and may never be). Here’s a sampling of the modern black hole bestiary.

Quantum Black Holes

Quantum black holes are hypothetical objects whose existence has been suggested but which have never been seen in nature. They are supposed to be black holes the size of elementary particles. They may have been created in the early stages of the Big Bang, when there was a lot of loose energy floating around. They may also have been created in collisions of high energy cosmic rays, although this is unlikely.

In any case, there is a process known as Hawking radiation that causes black holes to evaporate over time. The smaller the black hole, the faster the evaporation process. Even if quantum black holes were created in the Big Bang, then the chances are that they would have evaporated by now.

One interesting bit of silliness concerning quantum black holes occurred in 2008, when the Large Hadron Collider—the world’s largest particle accelerator—was going to be turned on in Geneva, Switzerland. In this machine, protons are accelerated to close to the speed of light and then allowed to collide head on. A group of activists argued that these collisions would create black holes that would consume the earth, and they went to federal court (in Hawaii, of all places) to prevent scientists from turning the machine on. The judge, thankfully, listened to scientists who pointed out that cosmic rays of much higher energy than those available at CERN had been bombarding Earth for 4.5 billion years without creating any black holes.

Primordial Black Holes

Primordial black holes are another type of black hole that have been talked about but never seen. Theorists have proposed the category because recent discoveries by the James Webb Space Telescope have indicated that supermassive black holes, about which more later, are present in the earliest galaxies we can see. This naturally raises the question of how those black holes got so big so fast. If some large black holes formed by some as yet unknown process in the Big Bang, it could answer this question.

Stellar Black Holes

Stellar black holes, having a mass typical of large stars, were the first to have been discovered. To understand how these black holes came to be we need to take a small astrophysical excursion and discuss how stars work.

Stars begin their life in the gas clouds that litter space. These clouds are lumpy in the sense that some regions have more mass than others. The extra gravitational attraction associated with that mass pulls more matter in, which increases the mass, which increases the gravitational attraction, and so on. Eventually that original lump becomes a massive sphere of gas being pulled together by its own gravity. The sphere heats up, and when it gets hot enough it initiates nuclear fusion reactions that turn hydrogen into helium, generating energy in the process. This energy streams outward, creating a pressure that balances the force of gravity. The star stabilizes and for the rest of its life burns its nuclear fuel to fight off the inward pull of gravity. The light that you see when you look at a star is what leaks out after the star has used the energy to fight off gravity. Think of it as the by-product of an epic battle.

Eventually the star loses. It runs out of fuel, while gravity just never quits. Depending on the mass of the star, there are a number of quantum mechanical processes that can prevent total collapse. For our purposes, we simply note that if the mass of the star is more than ten times the mass of the Sun, all of the material of the star will be pulled inside its Schwarzschild radius, and a stellar black hole will be born.

The historical debate about the existence of black holes was centered on this process, and consequently on the existence of stellar black holes. We should also point that it was the discovery of a stellar black hole that eventually proved that black holes actually exist.

Intermediate Mass Black Holes

Suppose you were doing a study of the age of people in a given population, and you discovered that there were a lot of people under twenty and a lot of people over fifty, but no one in between. You would immediately suspect that you were missing a part of the population and begin searching for thirty- and forty-year-olds.

Our situation concerning the masses of black holes is similar. We know of many stellar black holes with masses a few dozen times the mass of the Sun and we know of many black holes with masses of millions and even billions of times the mass of the Sun. The search for masses in between is just starting.

A research team headed by Shobita, using the James Webb Space Telescope, has found what may be an intermediate black hole in a nearby dwarf galaxy.

Supermassive Black Holes

No one expected this, but it turns out that at the heart of nearly every normal galaxy there is a black hole with a mass millions of times that of the Sun. We do not know how these black holes form, nor do we know the role they play in the formation and structure of galaxies. They are the most mysterious members of the black hole entourage, which is in and of itself the most mysterious collection of objects in the universe.

This raises an important question. We know that galaxies are the basic building blocks of the universe. We also know, thanks to the James Webb Space Telescope, that galaxies formed early in the life of the universe. At the moment we do not understand how large galaxies and their attendant supermassive black holes formed as quickly as they did. Thus, the study of supermassive black holes is intimately tied to understanding the processes by which the universe formed. The problem, of course is that we still have a lot to learn about both the formation of galaxies and the creation of supermassive black holes. Nevertheless, understanding the formation of the universe remains one of the deepest questions that modern scientists investigate.

We have known since that day in 1915 that black holes are predicted by general relativity. Since the discovery of supermassive black holes in the late twentieth century, we have learned that they are intimately tied to the formation and evolution of galaxies in the universe. It is unfortunate that Einstein died before any black holes were discovered and would never know the excitement his equations would generate.

Read more in Supermassive: Black Holes at the Beginning and End of the Universe, which is available from Smithsonian Books. Visit Smithsonian Books’ website to learn more about its publications and a full list of titles. 

Excerpt from Supermassive © 2025 by James Trefil and Shobita Satyapal