## 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 double star orbits were published when he was only sixteen years old. In 1891, Schwarzschild studied at the University of Strasbourg, and in 1893 he moved to the University of Munich, where he defended a thesis on equilibrium figures of rotating fluid masses, written under the direction of Hugo von Seeliger (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.^{1}^{1}endnote:
^{1}
For discussions of Poincaré’s
Wolfskehl lectures, see Rowe (2018, chap. 16),
Gray (2013, 416), and Walter
(2019). 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 to the Eastern Front, where he contracted a rare skin disease, from which he died in 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.^{2}^{2}endnote:
^{2}
See the bibliographical entry for
Arrhenius, and the study by
Kragh (2013).

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),
and the three volumes of *Collected Papers*
(Voigt, 1992a, b, c).

Time-stamp: "23.08.2021 20:29"

## References

- Mathematical Correspondences and Critical Editions. Springer, Cham. link2 Cited by: S. A. Walter (2019).
- Schwarzschild, Karl. See Dictionary of Scientific Biography, Volume 12: Ibn Rushd–Jean-Servais Stas, Gillispie, pp. 247–253. Cited by: 3-41. Karl Schwarzschild.
- Karl Schwarzschild. Monthly Notices of the Royal Astronomical Society 77 (4), pp. 314–319. link1 Cited by: 3-41. Karl Schwarzschild.
- Gedächtnisrede auf Karl Schwarzschild (1873–1916). See Physiker über Physiker II: Antrittsreden, Erwiderungen bei der Aufnahme von Physikern in die Berliner Akademie, Gedächchtnisreden, 1870 bis 1929, Kirsten and Körber, pp. 243–244. Cited by: 3-41. Karl Schwarzschild.
- Dictionary of Scientific Biography, Volume 12: Ibn Rushd–Jean-Servais Stas. Charles Scribner’s Sons, New York. Cited by: S. H. Dieke (1975).
- Henri Poincaré: A Scientific Biography. Princeton University Press, Princeton. link1 Cited by: endnote 1.
- Schwarzschild, Karl. See The Biographical Encyclopedia of Astronomers, Hockey, pp. 1034–1035. Cited by: 3-41. Karl Schwarzschild.
- Karl Schwarzschild. Astrophysical Journal 45, pp. 285–292. link1 Cited by: 3-41. Karl Schwarzschild.
- The Biographical Encyclopedia of Astronomers. Springer, New York. Cited by: P. Habison (2007).
- Statistical methods in stellar astronomy. See Congress of Arts and Science: Universal Exposition, St. Louis, 1904, Rogers, pp. 369–425. link1 Cited by: 3-41. Karl Schwarzschild.
- Physiker über Physiker II: Antrittsreden, Erwiderungen bei der Aufnahme von Physikern in die Berliner Akademie, Gedächchtnisreden, 1870 bis 1929. Akademie-Verlag, Berlin. Cited by: A. Einstein (1979).
- Nordic cosmogonies: Birkeland, Arrhenius and fin-de-siècle cosmical physics. European Physical Journal H 38 (4), pp. 549–572. link1 Cited by: endnote 2.
- Sur la stabilité de l’équilibre des figures piriformes affectées par une masse fluide en rotation. Philosophical Transactions of the Royal Society A 198, pp. 333–373. link1 Cited by: 3-41. Karl Schwarzschild.
- Leçons sur les hypothèses cosmogoniques. Hermann, Paris. link1 Cited by: 3-41. Karl Schwarzschild.
- Congress of Arts and Science: Universal Exposition, St. Louis, 1904. Houghton, Mifflin, Boston/New York. link1 Cited by: J. C. Kapteyn (1906).
- A Richer Picture of Mathematics: the Göttingen Tradition and Beyond. Springer, Cham. Cited by: endnote 1.
- Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. 6, Geodäsie, Geophysik, und Astronomie, Teil 2, Hälfte 1. Teubner, Leipzig. link1 Cited by: 3-41. Karl Schwarzschild.
- Die Poincaré’sche Theorie des Gleichgewichts einer homogenen rotierenden Flüssigkeitsmasse. Ph.D. Thesis, Ludwig-Maximilians-Universität zu München, Munich. Cited by: 3-41. Karl Schwarzschild.
- Die Poincaré’sche Theorie des Gleichgewichts einer homogenen rotierenden Flüssigkeitsmasse. Neue Annalen der königlichen Sternwarte in Bogenhausen bei München 3, pp. 231–299. link1 Cited by: 3-41. Karl Schwarzschild.
- Beiträge zur photographischen Photometrie der Gestirne. Publicationen der v. Kuffner’schen Sternwarte Wien 5, pp. C3–C135. Cited by: 3-41. Karl Schwarzschild.
- Ueber die Eigenbewegung der Fixsterne. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, mathematisch-physikalische Klasse, pp. 614–632. link1 Cited by: 3-41. Karl Schwarzschild.
- Leçons sur les hypothèses cosmogoniques by H. Poincaré. Astrophysical Journal 37, pp. 294–298. link1 Cited by: 3-41. Karl Schwarzschild.
- Collected Works of Karl Schwarzschild, Volume 1. Springer-Verlag, Berlin. Cited by: 3-41. Karl Schwarzschild.
- Collected Works of Karl Schwarzschild, Volume 2. Springer-Verlag, Berlin. Cited by: 3-41. Karl Schwarzschild.
- Collected Works of Karl Schwarzschild, Volume 3. Springer-Verlag, Berlin. Cited by: 3-41. Karl Schwarzschild.
- Poincaré-week in Göttingen, in light of the Hilbert-Poincaré correspondence of 1908–1909. See Mathematical Correspondences and Critical Editions, Borgato et al., pp. 297–310. link1, link2 Cited by: endnote 1.