Karl Schwarzschild


Born: 9 October 1873 in Frankfurt am Main, Germany
Died: 11 May 1916 in Potsdam, Germany


Karl Schwarzschild's parents were Henrietta Sabel and Moses Martin Schwarzschild. The family was Jewish, with Karl's father being a well-off member of the business community in Frankfurt. Dieke writes in [1]:-

From his mother, a vivacious, warm person, Schwarzschild undoubtedly inherited his happy, outgoing personality; from his father, a capacity for sustained hard work.

Karl was the oldest of his parents six children, having four younger brothers and one sister. He was part of a larger extended family of relatives, too, who were cultured people with interests mainly in art and music. He did not, however, get his love of science from his immediate or extended family since he became the first member of his family to become a scientist.

He attended a Jewish primary school in Frankfurt up to the age of eleven, then he entered the Gymnasium there. It was at this stage that he became interested in astronomy and saved his pocket money to buy himself materials such as lens from which he could construct a telescope. Karl's father was friendly with Professor J Epstein, who was professor at the Philanthropin Academy and had his own private observatory. Their friendship arose through a common interest in music. Professor Epstein has a son, Paul Epstein, who was two years older than Karl and the two boys became good friends. They shared an interest in astronomy, and Karl learnt how to use a telescope and also learnt some advanced mathematics from his friend Paul Epstein.

It was in large part what he learnt through his friendship with Epstein which led to Schwarzschild mastering celestial mechanics by the age of sixteen. Such was this mastery that he wrote his first two papers on the theory of orbits of double stars at this age while still at the Frankfurt Gymnasium. The papers were published in Astronomische Nachrichten in 1890.

Schwarzschild studied at the University of Strasbourg during the two years 1891-93 where he learnt a great deal of practical astronomy, then at the University of Munich where he obtained his doctorate. His dissertation, on an application of Poincaré's theory of stable configurations of rotating bodies to tidal deformation of moons and to Laplace's origin of the solar system, was supervised by Hugo von Seeliger. Schwarzschild found great inspiration from Seeliger's teaching which influenced him throughout his life.

After the award of his doctorate, Schwarzschild was appointed as an assistant at the Von Kuffner Observatory in Ottakring which is a suburb of Vienna. He took up his appointment in October 1896 and held it until June 1899. While at the Observatory he worked on ways to determine the apparent brightness of stars using photographic plates [4]:-

... a long and sustained investigation, which required much perfection of detail as well as brilliance of conception.

He left the Von Kuffner Observatory in June 1899 and became a Privatdozent at the University of Munich, having submitted his work on measuring stellar magnitudes as his habilitation thesis Beiträge zur photographischen Photometrie der Gestirne. This work led him to make several important discoveries. First he saw that the photographic magnitudes which he measured differed from the visual magnitudes which had been tabulated. He realised that the difference was due to different colours of the stars. Choosing 367 stars to measure from the Von Kuffner Observatory, he included two variable stars. The range of magnitude change as measured by his photographic methods was much greater than the range of change in visual magnitude. He realised, correctly, that this was due to changes in surface temperature of the variable star through its cycle.

At a meeting of the German Astronomical Society in Heidelberg in 1900 Schwarzschild discussed the possibility that space was non-Euclidean. In the same year he published a paper giving a lower limit for the radius of curvature of space as 2500 light years. He also worked on radiation pressure from the sun and, with the assumption that the tails of comets consisted of spherical particles which reflected light well, he calculated the size of the particles in the tails. He knew that radiation pressure had to overcome gravitation, and he also knew that the particles did not scatter light. This allowed him to deduce that the diameters of the particles had to be between 0.07 and 1.5 microns.

From 1901 until 1909 he was extraordinary professor at Göttingen and also director of the Observatory there. In Göttingen he collaborated with Klein, Hilbert and Minkowski. In less than a year he had been promoted to Ordinary Professor. Eddington writes in [4]:-

To a man of his wide interests in all branches of mathematics and physics the surroundings must have been very congenial ...

Schwarzschild published on electrodynamics and geometrical optics during his time at Göttingen. He carried out a large survey of stellar magnitudes while at the Göttingen Observatory, publishing Aktinometrie (the first part in 1910, the second in 1912). In 1906 he studied the transport of energy through a star by radiation and published an important paper on radiative equilibrium of the atmosphere of the sun. He married Else Posenbach, the daughter of a professor of surgery at Göttingen, on 22 October 1909. They had three children, Agathe, Martin who was born on 31 May 1912 and went on to became a professor of astronomy at Princeton, and Alfred.

After his marriage, near the end of 1909, Schwarzschild left Göttingen to take up an appointment as director of the Astrophysical Observatory in Potsdam. This was the most prestigious post available for an astronomer in Germany and he filled the position with great success. He had the opportunity to study photographs of the return of Halley's comet in 1910 taken by a Potsdam expedition to Tenerife. He also made major contributions to spectroscopy which became a topic of great interest to him around this time.

In 1913 Schwarzschild was elected to the Berlin Academy. In his admission speech he gave a good indication of his attitude towards science (see for example [4]):-

Mathematics, physics, chemistry, astronomy, march in one front. Whichever lags behind is drawn after. Whichever hastens ahead helps on the others. The closest solidarity between astronomy and the whole circle of exact science. ... from this aspect I may count it well that my interest has never been limited to the things beyond the moon, but has followed the threads which spin themselves from there to our sublunar knowledge; I have often been untrue to the heavens. That is an impulse to the universal which was strengthened unwittingly by my teacher Seeliger, and afterwards was further nourished by Felix Klein and the whole scientific circle at Göttingen. There the motto runs that mathematics, physics, and astronomy constitute one knowledge, which, like the Greek culture, is only comprehended as a perfect whole.

On the outbreak of war in August 1914 Schwarzschild volunteered for military service. He served in Belgium where he was put in charge of a weather station, France where he was assigned to an artillery unit and given the task of calculating missile trajectories, and then Russia.

While in Russia he wrote two papers on Einstein's relativity theory and one on Planck's quantum theory. The quantum theory paper explained that the Stark effect, namely the splitting of the spectral lines of hydrogen by an electric field (the amount being proportional to the field strength), could be proved from the postulates of quantum theory. This was proved independently by a P Epstein from Munich at almost the same time.

Schwarzschild's relativity papers give the first exact solution of Einstein's general gravitational equations, giving an understanding of the geometry of space near a point mass. He sent the first paper to Einstein who replied:-

I had not expected that one could formulate the exact solution of the problem in such a simple way.

The work presented in these two papers formed the basis for a later study of black holes, showing that bodies of sufficiently large mass would have an escape velocity exceeding the speed of light and so could not be seen. However, Schwarzschild himself makes clear that he believes that the theoretical solution is physically meaningless, so making it very clear that he did not believe in the physical reality of black holes.

He contracted an illness while in Russia called pemphigus, which is a rare autimmune blistering disease of the skin. For people with this disease the immune system mistakes the cells in the skin as foreign and attacks them causing painful blisters. In Schwarzschild's time there was no known treatment and, after being invalided home in March 1916, he died two months later.

Eddington writes in [4]:-

The wide range of his contributions to knowledge suggests a comparison with Poincaré; but Schwarzschild's bent was more practical, and he delighted as much in the design of instrumental methods as in the triumphs of analysis. ... his joy was to range unrestricted over the pastures of knowledge, and, like a guerrilla leader, his attacks fell where they were least expected.

Since Schwarzschild died at age 42 at the height of his achievements, it is not too surprising that he received relatively few honours in his lifetime. He was, however, elected to the Scientific Society of Göttingen in 1905, the Royal Astronomical Society of London on 11 June 1909, and the German Academy of Sciences in 1913. He did receive posthumous honours too, in particular an observatory, founded in 1960 in Tautenburg as an affiliated Institute of the German Academy of Sciences, was named after him. The dedication described him as:-

... the greatest German astronomer of the last hundred years.

After the reunification of Germany, the Institute was refounded in 1992 and renamed "Thüringer Landessternwarte 'Karl Schwarzschild' Tautenburg". The German Astronomical Society established a special lectureship in his honour in 1959 and a Karl Schwarzschild Medal. The first recipient was Martin Schwarzschild, his son.

Article by: J J O'Connor and E F Robertson

October 2003


MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Schwarzschild.html]