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3-41. Karl Schwarzschild

Karl Schwarzschild (1873–1916) got an early start in astronomy and celestial mechanics in Frankfurt, thanks to his father’s acquaintance with the mathematician Paul Epstein. His first two papers on binary-star orbits were published when he was only sixteen years old. In 1891, Schwarzschild began studies at the Kaiser-Wilhelm University of Strasbourg, where he observed variable stars under the guidance of Ernst Becker, and heard lectures by E. B. Christoffel (Raap, 2017). In 1893 he moved to Munich for a year of military service, while enrolling at the University of Munich, where he heard lectures by Ferdinand Lindemann, and the director of the Munich Observatory, Hugo von Seeliger. Under the latter’s direction, Schwarzschild defended a thesis on equilibrium figures of rotating fluid masses (Schwarzschild, 1896, 1898).

From 1896 to 1899, Schwarzschild was an assistant at the Kuffner Observatory in Ottakring (near Vienna), where he worked on photometric techniques, a subject on which he presented his Habilitation in 1899 at the University of Munich, entitled “Beiträge zur photographischen Photometrie der Gestirne” (Schwarzschild, 1900).

In October, 1901 Schwarzschild was named associate professor of astronomy at the University of Göttingen, and director of the Göttingen Observatory, after von Seeliger and Max Wolf both declined offers. In May of the next year he was promoted to full professor. In Göttingen, Schwarzschild participated in research seminars with the leading lights of mathematics and theoretical physics, including his colleagues David Hilbert, Hermann Minkowski, Emil Wiechert, Karl Runge, Woldemar Voigt, and Felix Klein, and a number of brilliant doctoral students and Privatdozenten, including Max Born and Walter Ritz. He was charged with editing the astronomical part of the volume on geodesy, geophysics, and astronomy in Felix Klein’s six volume project, the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen (Schwarzschild et al., 1905). Along with Klein (§ 4-47-39), Schwarzschild had hoped Poincaré would not only attend, but would also encourage young French theoretical astronomers to participate in the meeting of the Astronomical Society. The meeting was held in early August, 1902, in Göttingen (§ 3-41-1); Poincaré did not attend. In April, 1909, Schwarzschild attended Poincaré’s Wolfskehl lectures in Göttingen. Later the same year, he left Göttingen to direct the Potsdam Observatory.

In 1913, Schwarzschild became a member of the German Academy of Science in Berlin. When war broke out, he volunteered, and was assigned first to a meteorological unit in Namur, Belgium, and then to the staff of an artillery unit in France. This work gave rise to a paper on the effect of wind velocity and air density on missile trajectories. Lieutenant Schwarzschild was transferred to the Eastern Front, where he contracted a rare skin disease known as pemphigus. The symptoms were debilitating, and resulted in his release from military service and return to Potsdam, where he died on 11 May, 1916.

Beginning with his dissertation, Schwarzschild engaged with Poincaré’s work in celestial mechanics on several occasions, and paid tribute to both its power, and opacity. The letter that we publish here is his response to Poincaré’s memoir on the stability of the pear-shaped figure (Poincaré 1902), that developed out of Poincaré’s exchange with George Howard Darwin.

Like Poincaré, Schwarzschild took a keen interest in Kapteyn’s announcement of his two-stream theory of star flows in the Milky Way (1906). He published an alternative, unitary model of the proper motion of stars, based on an ellipsoidal velocity distribution (Schwarzschild 1907).

Poincaré did not mention Schwarzschild’s theory in his Leçons sur les hypothèses cosmogoniques (Poincaré 1911), an omission which may have led Schwarzschild in his review to deplore Poincaré’s preference for French authors. He also sharpened Poincaré’s critique of Arrhenius’ hypothesis of an eternally cyclic universe, where the pressure of radation countered the attraction of gravitation, which ran counter to the second law of thermodynamics.

Schwarzschild expressed admiration for Poincaré’s critical approach. In his discussions of cosmogonical hypotheses, Schwarzschild wrote, Poincaré had not “destroyed these ideas by criticism, but laid bare their core and even represented many of them in a clearer way than their authors” (Schwarzschild 1913).

Schwarzschild was compared to Poincaré by Eddington, in virtue of his wide-ranging scientific contributions; Eddington paid tribute to Schwarzschild’s intellectual penetration, describing him as a “guerilla leader”, whose “attacks fell where they were least expected” (Eddington 1917, 319). For a contemporary overview of Schwarzschild’s life and work by a close collaborator, see Hertzsprung (1917); see also the notice by Einstein (1979), the DSB article by Dieke (1975)), Habison (2007), the three volumes of Collected Papers (Voigt, 1992a, b, c), and the volume edited by Reinsch and Wittmann (2017).

Time-stamp: "22.08.2025 12:24"

Notes

• 1 For discussions of Poincaré’s Wolfskehl lectures, see Rowe (2018, chap. 16), Gray (2013, 416), and Walter (2018).
• 2 See the bibliographical entry for Arrhenius, and the study by Kragh (2013).