Karl Schwarzschild

Karl Schwarzschild was born on October 9, 1873 in Frankfurt am Main, the eldest of six children in a prosperous Jewish family with a long line of merchants and artists but no scientists. The mathematical talent showed early and was hard to miss. By eleven he was reading textbooks on celestial mechanics for pleasure. At sixteen, while still a Gymnasium pupil, he wrote two papers on the orbits of binary stars and on the determination of orbits from three observations, both serious enough that the Astronomische Nachrichten published them. The young Schwarzschild’s father, a businessman who knew his own limits, sought out the Frankfurt astronomer Johann Epstein and asked what to do with a child who treated Kepler’s equation as light reading. Epstein gave him a telescope and the run of the observatory and told the father to get out of the way.

He went up to Strasbourg and then to Munich, where he took his doctorate in 1896 at twenty-two on the equilibrium figures of rotating fluid bodies, a Poincaré problem at the boundary between mathematics and astrophysics. By twenty-eight he was professor of astronomy at Göttingen, the most concentrated mathematical town in Europe, working alongside Felix Klein and David Hilbert. By thirty-six he had been called to direct the Potsdam Observatory, the most senior astronomical post in Germany. His range was already unusual. He invented photographic photometry and used it to measure the brightnesses of thousands of stars. He worked out the theory of radiative equilibrium in stellar atmospheres, the framework still used today. He published on geometrical optics, on the Stark effect, on the orbits of comets, on the statistical distribution of stellar velocities. There was no obvious thing he could not do.

In August 1914 Germany went to war and Schwarzschild, at forty, volunteered. He was not conscripted. He was a comfortable professor, the director of a national observatory, and well past the age at which any army wanted him. He volunteered anyway. The reason he gave was duty as a German Jew, whose people had been granted full civic rights only two generations earlier and were now expected to demonstrate them on the battlefield. He served first at a weather station in Belgium, then with an artillery unit in France, and finally on the Russian front, where his job was to compute trajectories for the long-range guns. The mathematics of ballistics is the mathematics of orbits with friction, and Schwarzschild was overqualified for it.

In November 1915, in the trenches near the Russian front, he read Einstein’s freshly published paper on general relativity. Einstein had given the field equations but had not yet found an exact solution. He had only an approximation good enough to predict the perihelion precession of Mercury, and he was openly doubtful that the full nonlinear equations could ever be solved in closed form. Schwarzschild, between artillery calculations, set himself to the simplest non-trivial case: the gravitational field outside a single, isolated, non-rotating, spherically symmetric mass. Within weeks he had it. The solution is one of the most compact and consequential equations in twentieth-century physics, and it had been derived on field paper, by candlelight, in a war zone.

He mailed the manuscript to Einstein on December 22, 1915. Einstein replied a few days later, plainly astonished. He had not expected a closed-form solution to be possible at all, and he had certainly not expected one to arrive in the post from an officer at the front. I had not expected, he wrote, that the exact solution to the problem could be formulated. Your analytical treatment of the problem appears to me splendid. Einstein read the paper aloud to the Berlin Academy on January 13, 1916 in Schwarzschild’s name. A second paper, on the interior solution for a uniform-density sphere, followed in February. Together they remain the foundation of every calculation in classical general relativity.

Karl Schwarzschild (; 9 October 1873 – 11 May 1916) was a German physicist and astronomer.

What the solution describes is the geometry of empty space around a concentrated mass. Far from the mass, space and time look almost flat and Newton’s law of gravitation emerges as the leading approximation. Closer in, the geometry curves, clocks run slow, and light bends. At one particular radius, the quantity now called the Schwarzschild radius and equal to 2GM/c², something strange happens to the coordinates: a term in the metric becomes infinite. For the sun this radius is about three kilometers, well inside the actual radius of the sun, and so the singularity sits harmlessly inside ordinary matter and was for decades dismissed as a mathematical artifact. Schwarzschild himself did not believe any real object could be small enough to expose it. The phrase black hole was forty years in the future, and the realization that the Schwarzschild radius marks a one-way membrane through which nothing, not even light, can escape would wait until the work of Oppenheimer and Snyder in 1939 and the modern reformulation by Kruskal and Szekeres in 1960.

The price of the work was his life. While at the front he contracted pemphigus, a brutal autoimmune disease of the skin and mucous membranes, untreatable in 1916 and almost certainly worsened by the conditions in which he was living. He was invalided home in March, after his two relativity papers had been delivered to Berlin. He died at Potsdam on May 11, 1916, two months after his second paper appeared, at the age of forty-two. He left a wife, three children, and an eleven-year-old son, Martin, who would grow up to be one of the founding figures of modern astrophysics in his own right and a refugee from the Nazi Germany that killed the rest of the extended family.

At the outbreak of World War I in 1914, Schwarzschild volunteered for service in the German army despite being over 40 years old. He served on both the western and eastern fronts, specifically helping with ballistic calculations and rising to the rank of second lieutenant in the artillery. While serving on the front in Russia in 1915, he began to suffer from pemphigus, a rare and painful autoimmune skin-disease. In…

For this book Schwarzschild matters less for any direct contribution to quantum mechanics than for the model of physics his career embodies. The same year Einstein wrote down the field equations of curved spacetime, a serving officer on the eastern front read the paper, solved them exactly for the simplest interesting case, and mailed the answer back. The radius that bears his name is the boundary of the holes from which Hawking would, sixty years later, extract the quantum radiation that is still the deepest known link between gravity and the quantum world.