###### By Dan Hooper, Ph.D., University of Chicago

## Of all of the concepts to come out of modern physics—or even out of all of science—none have captured our imagination as much as black holes. From *Star Trek* to *Interstellar*, they are a staple of science fiction.

Dozens of popular books have been written about these strange and fascinating objects by authors ranging from Kip Thorne and Stephen Hawking to Neil deGrasse Tyson. Black holes are, in fact, a direct consequence of Einstein’s Theory of General Relativity.

But Einstein himself never realized or accepted this fact.

This is a transcript from the video series

What Einstein Got Wrong. Watch it now, on The Great Courses Plus.

In the paper that he wrote in 1915 introducing the Theory of General Relativity, Einstein used the field equations of his theory to make a series of different predictions. Most notably, these predictions included Einstein’s calculation of Mercury’s orbit, which agreed well with the observations while the equations of Newtonian gravity did not.

Learn more about Einstein’s general theory of relativity

### Solving Einstein’s Field Equations

Einstein’s field equations are notoriously difficult to manipulate, even for physicists who are experts in relativity. Technically speaking, it is because these equations are nonlinear. This means that when you change one input, you end up changing many other things as well.

Einstein himself originally thought these equations couldn’t be solved precisely. Instead, he found mathematical techniques to identify approximate solutions. Today, physicists often employ the help of powerful computers to solve these ruthlessly formidable equations.

It turns out, however, that in some special and simple cases, exact solutions to Einstein’s field equations do exist. The first person to find one of these exact solutions was not Einstein himself, or even another leading scientist from among the German universities, to which general relativity was first widely disseminated.

Instead, the first exact solution came from a German lieutenant, fighting in the trenches of the Russian front of World War I. This lieutenant was an astronomer and mathematician named Karl Schwarzschild.

When World War I broke out in 1914, Schwarzschild was the director of the Astrophysical Observatory in Potsdam. Despite being 41-years-old at the time, Schwarzschild volunteered for military service shortly after hostilities began.

Over the next several months, he put his mathematical abilities to use for the German army, calculating the trajectories of artillery shells, and in the process, seeing action in France, Belgium and Russia.

While in the trenches of the Eastern Front, Schwarzschild somehow got his hands on a copy of the most recent issue of the *Proceedings of the Royal Prussian Academy of Sciences*, which included a brief account by Einstein describing his new Theory of General Relativity.

From the contents of this article, Schwarzschild became one of the first physicists to learn to skillfully manipulate the equations of Einstein’s new theory. In his exploration of general relativity, Schwarzschild focused on an extremely simple—albeit physically important—case.

Learn more about what Einstein got right: special relativity

### Soldier Discovers a Simple Solution

Schwarzchild imagined a situation with a spherical mass—like a perfectly round star or a planet—that wasn’t rotating or otherwise changing. For this simple case, Schwarzschild calculated the effects of gravity using Einstein’s field equations.

Far away from the spherical mass, Schwarzschild found that gravity acts in the same way that Isaac Newton had predicted more than two centuries before. But as you move in closer to the spherical mass, Schwarzschild’s solution begins to depart from the Newtonian prediction.

Among other things, Schwarzschild’s solution showed that Einstein’s theory could perfectly explain the long-standing discrepancy observed in the orbit of Mercury. By finding the exact solution for Mercury’s orbit—rather than Einstein’s approximate solution—Schwarzschild demonstrated with greater rigor that observations of Mercury favored general relativity over Newtonian gravity.

In December of 1915, Schwarzschild wrote a letter to Einstein, describing the solution he had discovered to the field equations. The next month, Einstein wrote back to Schwarzschild and shortly thereafter presented the new solution at a meeting of the Prussian Academy.

Einstein was very pleased—albeit surprised—that such a simple and exact solution could be found. Einstein had previously thought that the nonlinearity of his field equations would make it impossible to find any exact solutions, but upon examining Schwarzschild’s letter, Einstein happily conceded that he was mistaken—at least in this special case.

Learn more about why general relativity is inconsistent with a static universe

### Schwarzschild’s Predictions About Spacetime

Over the next few months, Schwarzschild wrote two papers on general relativity, which among other things, detailed his important and exact solution to the field equations. Despite the ongoing hardships of war, Schwarzschild was at the peak of his scientific skills and achievements.

Tragically, in March of 1916, Schwarzschild came down with a rare skin disease, that caused his immune system to attack his own skin cells, leading to painful blistering and other symptoms. Two months later, Schwarzschild died, never to see the legacy of his work.

The Schwarzschild solution to the field equations is famous today not because it was the first exact solution of general relativity, or because it predicts the orbit of Mercury correctly. It is most often talked about today because of some of the other interesting and bizarre predictions it makes.

According to Schwarzschild’s solution, if you could compress enough mass into a small enough volume, the geometry of the surrounding space would go haywire, and spacetime itself would become infinitely curved. The radius around an object at which the spacetime becomes infinitely curved is known as the “Schwarzschild radius,” and it is proportional to the mass of the object.

For example, if the mass of the entire Sun were compressed from its current radius of 430,000 miles into a radius of only 1.9 miles, the space around it would become infinitely curved.

For an object with the mass of the Earth, the Schwarzschild radius is about a third of an inch. This infinite curvature would prevent anything, even including light, from ever passing through the Schwarzschild radius.

To a stationary observer viewing such an object from the outside, the infinite curvature of space means that it would take an infinitely long time for anything to pass through the Schwarzschild radius.

Therefore, nothing can ever escape from or reach such an object. Decades later, physicists would begin to call these objects by the name we use today—black holes.

Learn more about Einstein’s devotion to the principle of determinism

### Skepticism on the Existence of Black Holes

Einstein seemed to give little thought to the possibility that such exotic objects might exist. He instead focused on more pragmatic issues, such as comparing the predictions of the Schwarzschild solution to the observations of Mercury’s orbit.

At the time, there were good reasons for scientists to be skeptical that black holes exist. Even if a black hole could hypothetically form if there were enough mass compressed into a small enough volume of space, this doesn’t mean that it has ever happened.

Even if there were a law of physics that said a unicorn is born every time the Queen of England does a jig on the North Pole, this wouldn’t mean that there are any unicorns in our universe today. Maybe a black hole could in principle be formed, but in practice maybe it has never formed.

Furthermore, most physicists at the time thought that there would likely be things that would prevent a black hole from forming, even in principle. After all, there was a lot of uncharted territory between the kinds of stars that had been observed, and the kinds of conditions that could potentially lead to the formation of a black hole.

Learn more about the paradoxical quantum phenomenon called entanglement

There could very well have been new laws of physics yet to be discovered that would somehow prevent black holes from forming in the real world. It was far from obvious at the time that black holes did, or even could, exist.

In 1916, Einstein was not alone in doubting that black holes were real.

### Common Questions About Einstein’s Views on Black Holes

**Q: What exactly were Einstein’s views on black holes?**

Einstein denied that black holes could exist and published a paper arguing his point.

**Q: Do black holes die?**

It is currently thought that black holes do evaporate and disappear, but any current black holes would take longer than the life of the universe to do so.

**Q: How were black holes discovered?**

Karl Schwarzschild had developed math while solving Einstein’s general relativity equations that hinted at a Schwarzschild radius where gravity went into a singularity in the center of large masses. This was extrapolated over the years until observations were made that appear to back up the predictions about black holes, and one was observed in 1971.

**Q: Did Einstein discover black holes?**

Einstein did not discover black holes, but his unproven equations describing general relativity predicted their existence.