Science Library - free educational site

Karl Schwarzschild

1873 - 1916

Karl Schwarzschild, 1873 - 1916

Karl Schwarzschild was a German astronomer and physicist, and a pioneer of the field of astrophysics. He solved Einstein's field equations while serving as an artillery office on the Eastern Front, during World War One.

  • Nationality
  • German

  • Subject
  • Astronomy

  • Fields
  • Astrophysics, field theory, General Relativity, electrodynamics, optics

  • Distinctions
  • Member of the Prussian Science Academy, 1912.

    The Karl-Schwarzschild-Observatorium is in Thüringen, Germany.

    There is an asteroid called Schwarzschilda.

    Streets in Berlin, Göttingen und Garching bei München are named after him.

  • Posts
  • Professor and Director of the Sternwarte Göttingen (Göttingen Observatory), 1901 - 1909, where he worked with David Hilbert and Hermann Minkowski.

    Director of the Astrophysikalisches Observatorium in Potsdam, 1909.

  • Publications
  • Untersuchungen zur geometrischen Optik I, II, II., 1906. (Investigation of geometrical optics, volumes I, II, III).

    Schwarzschild published many papers on astronomical subjects, such as the sun's atmosphere, the bending of light through a slit, electrodynamics, electron motion, fixed star motion, Halley's comet (1911), and the 'new mechanics'.

    But his most important work is arguably on Einstein's theories of relativity, in particular the field equations, published in January 1916.

    Über das Gravitationsfeld eines Massenpunktes nach der Einstein’schen Theorie, 1916 (On the gravitational field of a point mass according the Einstein's Theory).

    Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit, 1916 (On the gravitational field of a sphere of incompressible liquid, according to Einstein's Theory).

  • Theories
  • Astrophotography: he derived equations for the relationship between starlight intensity, exposure times and photoplate emulsion optical density, in which he derives the formula with the Schwarzschild Exponent.

    The Schwarzschild solution: Exact solutions to the field equations for Einstein's General Relativity.

    The Inner Schwarzschild solution: a general solution applicable to any incompressible fluid.

    Schwarzschild radius and Schwarzschild black hole, formed by the gravitational collapse, with spherical symmetry, of a body to within the boundary of the Schwarzschild radius.

  • Equations
  • $i = f(I⋅ t^p)$, $i$ is the optical density of exposed photographic emulsion, $I$ the intensity of the starlight, $t$ the exposure time, $p$ is the Schwarzschild Exponent, which is dependent on the photographic plate, and is always < 1.

    Schwarzschild was the first to express the electromagnetic field in Lagrangian form.

    Field free variational formulation of electrodynamics.

    Schwarzschild radius: $R_s = {2GM}/{c^2}$, $G$ is the gravitational constant, $M$ is the mass, $c$ is the speed of light in a vacuum. $R_s$ is the boundary between the Schwarzschild interior and exterior solutions, a locus of points in space around the central mass $M$, within which everything, including photons, must fall into the central Mass.

Schwarzschild is known as the grandfather of black hole theory. He did not term the phrase (attributed to John Wheeler, 1960s), but is solution to the Einstein General Relativity field equations led to the mathematical calculation of the Schwarzschild radius - the set of points equidistant from a mass that is compressed as much as possible, at which the gravity is so intense, that the consequent bending of spacetime does not permit light to escape.

Karl Schwarzschild, 1873 - 1916
Karl Schwarzschild, 1873 - 1916, who solved Einstein's field equations

Tragically, this gentle genius died on May 11, 1916, of an auto-immune skin disease (Pemphigus vulgaris) he contracted in the trenches soon after sending his famous solution to Einstein. He was invalided back to Germany in March 1916, but died on 11 May 1916.

Karl Schwarzschild's son, Martin, born 1912, fled nazi-Germany in 1935, and settled in the USA, where he was an astrophysicist from 1947 at Princeton University. It is pleasing to see that he was able to continue his father's work at the same time and place as Einstein, whom his father had helped so much establish his General Relativity.

Latest Item on Science Library:

The most recent article is:

Air Resistance and Terminal Velocity

View this item in the topic:


and many more articles in the subject:

Subject of the Week


Information Technology, Computer Science, website design, database management, robotics, new technology, internet and much more. JavaScript, PHP, HTML, CSS, Python, ... Have fun while learning to make your own websites with

Computer Science

Great Scientists

Linus Pauling

1901 - 1994

Linus Pauling is the only person in history to have won two unshared Nobel Prizes (Chemistry 1954, Peace 1962). He is considered one of the greatest scientists and humanitarians ever, and his fields of activity were widespread.

Linus Pauling
IT Forum by Sean Bone

Quote of the day...

If you want a helping hand, you will find one at the end of your arm.