Karl Schwarzschild (; 9 October 1873 – 11 May 1916) was a German
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate caus ...
and astronomer.
Schwarzschild provided the first
exact solution to the
Einstein field equations
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
The equations were published by Einstein in 1915 in the form ...
of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, for the limited case of a single spherical non-rotating mass, which he accomplished in 1915, the same year that Einstein first introduced general relativity. The
Schwarzschild solution
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...
, which makes use of
Schwarzschild coordinates In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of ''nested round spheres''. In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coord ...
and the
Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...
, leads to a derivation of the
Schwarzschild radius
The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic ...
, which is the size of the
event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s.
In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact obj ...
of a non-rotating
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
.
Schwarzschild accomplished this while serving in the German army during
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
. He died the following year from the
autoimmune disease
An autoimmune disease is a condition arising from an abnormal immune response to a functioning body part. At least 80 types of autoimmune diseases have been identified, with some evidence suggesting that there may be more than 100 types. Nearly a ...
pemphigus
Pemphigus ( or ) is a rare group of blistering autoimmune diseases that affect the skin and mucous membranes.
The name is derived from the Greek root ''pemphix'', meaning "pustule".
In pemphigus, autoantibodies form against desmoglein, whi ...
, which he developed while at the
Russian front. Various forms of the disease particularly affect people of
Ashkenazi Jewish
Ashkenazi Jews ( ; he, יְהוּדֵי אַשְׁכְּנַז, translit=Yehudei Ashkenaz, ; yi, אַשכּנזישע ייִדן, Ashkenazishe Yidn), also known as Ashkenazic Jews or ''Ashkenazim'',, Ashkenazi Hebrew pronunciation: , singu ...
origin.
Asteroid
837 Schwarzschilda
837 Schwarzschilda, provisional designation 1916 AG, is a low-eccentric, well-observed asteroid from the asteroid belt, orbiting the Sun with a period of 3.48 years at a distance of 2.21–2.39 AU. It was discovered by German astronomer Max Wol ...
is named in his honour, as is the large crater
''Schwarzschild'', on the far side of the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
.
Life
Karl Schwarzschild was born on 9 October 1873 in
Frankfurt on Main, the eldest of six boys and one daughter,
to
Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
parents. His father was active in the
business community of the city, and the family had ancestors in Frankfurt from the sixteenth century onwards. The family owned two fabric stores in Frankfurt. His brother
Alfred
Alfred may refer to:
Arts and entertainment
*''Alfred J. Kwak'', Dutch-German-Japanese anime television series
* ''Alfred'' (Arne opera), a 1740 masque by Thomas Arne
* ''Alfred'' (Dvořák), an 1870 opera by Antonín Dvořák
*"Alfred (Interlu ...
became a painter. The young Schwarzschild attended a Jewish primary school until 11 years of age and then the
Lessing-Gymnasium (secondary school). He received an all-encompassing education, including subjects like Latin, Ancient Greek, music and art, but developed a special interest in
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
early on. In fact he was something of a child prodigy, having two papers on binary orbits (
celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
) published before the age of sixteen.
After graduation in 1890 he attended the
University of Strasbourg
The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers.
The French university traces its history to the ea ...
to study astronomy. After two years he transferred to the
Ludwig Maximilian University of Munich
The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's sixth-oldest university in continuous operatio ...
where he obtained his doctorate in 1896 for a work on
Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
's theories.
From 1897, he worked as assistant at the
Kuffner Observatory
The Kuffner observatory is one of two telescope-equipped public astronomical observatories situated in Austria's capital, Vienna. It is situated in the West of the city's Ottakring district, on the slope of the Gallitzinberg at 302 m altitude. ...
in Vienna. His work here concentrated on the
photometry Photometry can refer to:
* Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision
* Photometry (astronomy), the measurement of the flux or intensity of an astronomical object's electro ...
of star clusters and laid the foundations for a formula linking the intensity of the starlight, exposure time, and the resulting contrast on a
photographic plate
Photographic plates preceded photographic film as a capture medium in photography, and were still used in some communities up until the late 20th century. The light-sensitive emulsion of silver salts was coated on a glass plate, typically thinn ...
. An integral part of that theory is the
Schwarzschild exponent (
astrophotography
Astrophotography, also known as astronomical imaging, is the photography or imaging of astronomical objects, celestial events, or areas of the night sky. The first photograph of an astronomical object (the Moon) was taken in 1840, but it was no ...
). In 1899 he returned to Munich to complete his
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...
.
From 1901 until 1909 he was a professor at the prestigious
Göttingen Observatory
Göttingen Observatory (''Universitätssternwarte Göttingen'' (Göttingen University Observatory) or ''königliche Sternwarte Göttingen'' (Royal Observatory Göttingen)) is a German astronomical observatory located in Göttingen, Lower Saxony, Ge ...
within the
University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...
, where he had the opportunity to work with some significant figures, including
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
and
Hermann Minkowski
Hermann Minkowski (; ; 22 June 1864 – 12 January 1909) was a German mathematician and professor at Königsberg, Zürich and Göttingen. He created and developed the geometry of numbers and used geometrical methods to solve problems in number t ...
. Schwarzschild became the director of the observatory. He married Else Rosenbach, a great-granddaughter of
Friedrich Wöhler
Friedrich Wöhler () FRS(For) HonFRSE (31 July 180023 September 1882) was a German chemist known for his work in inorganic chemistry, being the first to isolate the chemical elements beryllium and yttrium in pure metallic form. He was the firs ...
and daughter of a professor of surgery at Göttingen, in 1909. Later that year they moved to
Potsdam
Potsdam () is the capital and, with around 183,000 inhabitants, largest city of the German state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the River Havel, a tributary of the Elbe, downstream of B ...
, where he took up the post of director of the Astrophysical Observatory. This was then the most prestigious post available for an astronomer in Germany.
From 1912 Schwarzschild was a member of the
Prussian Academy of Sciences
The Royal Prussian Academy of Sciences (german: Königlich-Preußische Akademie der Wissenschaften) was an academy established in Berlin, Germany on 11 July 1700, four years after the Prussian Academy of Arts, or "Arts Academy," to which "Berlin ...
.
At the outbreak of
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
in 1914 Schwarzschild volunteered for service in the
German army
The German Army (, "army") is the land component of the armed forces of Germany. The present-day German Army was founded in 1955 as part of the newly formed West German ''Bundeswehr'' together with the ''Marine'' (German Navy) and the ''Luftwaf ...
, 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
Pemphigus ( or ) is a rare group of blistering autoimmune diseases that affect the skin and mucous membranes.
The name is derived from the Greek root ''pemphix'', meaning "pustule".
In pemphigus, autoantibodies form against desmoglein, whi ...
, a rare and painful autoimmune skin-disease.
Nevertheless, he managed to write three outstanding papers, two on the
theory of relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
and one on
quantum theory
Quantum theory may refer to:
Science
*Quantum mechanics, a major field of physics
*Old quantum theory, predating modern quantum mechanics
* Quantum field theory, an area of quantum mechanics that includes:
** Quantum electrodynamics
** Quantum ...
. His papers on relativity produced the first exact solutions to the
Einstein field equations
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
The equations were published by Einstein in 1915 in the form ...
, and a minor modification of these results gives the well-known solution that now bears his name — the
Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...
.
In March 1916 Schwarzschild left military service because of his illness and returned to
Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...
. Two months later, on May 11, 1916, his struggle with pemphigus may have led to his death at the age of 42.
He rests in his family grave at the
Stadtfriedhof Göttingen.
With his wife Else he had three children:
*
Agathe Thornton
Agathe Henriette Franziska Thornton (née Schwarzschild; 20 November 1910 – 21 October 2006) was a New Zealand academic specialising in classics and Māori studies. She was born in Germany and moved to New Zealand in 1947. She taught in the cla ...
(1910-2006) emigrated to Great Britain in 1933. In 1946 she moved to New Zealand, where she became a classics professor at the
University of Otago
, image_name = University of Otago Registry Building2.jpg
, image_size =
, caption = University clock tower
, motto = la, Sapere aude
, mottoeng = Dare to be wise
, established = 1869; 152 years ago
, type = Public research collegiate u ...
in Dunedin.
*
Martin Schwarzschild
Martin Schwarzschild (May 31, 1912 – April 10, 1997) was a German-American astrophysicist.
Biography
Schwarzschild was born in Potsdam into a distinguished German Jewish academic family. His father was the physicist Karl Schwarzschild and ...
(1912-1997) became a professor of astronomy at
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
.
* Alfred Schwarzschild (1914-1944) remained in Nazi Germany and was murdered during the
Holocaust
The Holocaust, also known as the Shoah, was the genocide of European Jews during World War II. Between 1941 and 1945, Nazi Germany and its collaborators systematically murdered some six million Jews across German-occupied Europe; a ...
.
Work
Thousands of dissertations, articles, and books have since been devoted to the study of Schwarzschild's solutions to the
Einstein field equations
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
The equations were published by Einstein in 1915 in the form ...
. However, although his best known work lies in the area of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, his research interests were extremely broad, including work in
celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
, observational stellar
photometry Photometry can refer to:
* Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision
* Photometry (astronomy), the measurement of the flux or intensity of an astronomical object's electro ...
,
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, instrumental
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
, stellar structure, stellar
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
,
Halley's comet
Halley's Comet or Comet Halley, officially designated 1P/Halley, is a short-period comet visible from Earth every 75–79 years. Halley is the only known short-period comet that is regularly visible to the naked eye from Earth, and thus the o ...
, and
spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
.
[Eisenstaedt, “The Early Interpretation of the Schwarzschild Solution,” in D. Howard and J. Stachel (eds), Einstein and the History of General Relativity: Einstein Studies, Vol. 1, pp. 213-234. Boston: Birkhauser, 1989.]
Some of his particular achievements include measurements of
variable star
A variable star is a star whose brightness as seen from Earth (its apparent magnitude) changes with time. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as ...
s, using photography, and the improvement of optical systems, through the perturbative investigation of geometrical aberrations.
Physics of photography
While at Vienna in 1897, Schwarzschild developed a formula, now known as the
Schwarzschild law, to calculate the optical density of photographic material. It involved an exponent now known as the Schwarzschild exponent, which is the
in the formula:
(where
is optical density of exposed photographic emulsion, a function of
, the intensity of the source being observed, and
, the exposure time, with
a constant). This formula was important for enabling more accurate photographic measurements of the intensities of faint astronomical sources.
Electrodynamics
According to
Wolfgang Pauli
Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics fo ...
(Theory of relativity), Schwarzschild is the first to introduce the correct
Lagrangian
Lagrangian may refer to:
Mathematics
* Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier
** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...
formalism of the electromagnetic field
[K. Schwarzschild, Nachr. ges. Wiss. Gottingen (1903) 125] as
where
are the electric and applied magnetic fields,
is the vector potential and
is the electric potential.
He also introduced a field free variational formulation of electrodynamics (also known as "action at distance" or "direct interparticle action") based only on the world line of particles as
[K. Schwarzschild, Nachr. ges. Wiss. Gottingen (1903) 128,132]
where
are the world lines of the particle,
the (vectorial) arc element along the world line. Two points on two world lines contribute to the Lagrangian (are coupled) only if they are a zero Minkowskian distance (connected by a light ray), hence the term
. The idea was further developed by Tetrode
and Fokker in the 1920s and Wheeler and Feynman in the 1940s and constitutes an alternative/equivalent formulation of electrodynamics.
Relativity
Einstein himself was pleasantly surprised to learn that the
field equations
A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum ...
admitted exact solutions, because of their ''prima facie'' complexity, and because he himself had produced only an approximate solution.
Einstein's approximate solution was given in his famous 1915 article on the advance of the perihelion of Mercury. There, Einstein used rectangular coordinates to approximate the gravitational field around a spherically symmetric, non-rotating, non-charged mass. Schwarzschild, in contrast, chose a more elegant "polar-like" coordinate system and was able to produce an exact solution which he first set down in a letter to Einstein of 22 December 1915, written while he was serving in the war stationed on the Russian front. He concluded the letter by writing: "As you see, the war treated me kindly enough, in spite of the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas."
[Letter from K Schwarzschild to A Einstein dated 22 December 1915, in "The Collected Papers of Albert Einstein", vol.8a, doc.#169]
(Transcript of Schwarzschild's letter to Einstein of 22 Dec. 1915)
. In 1916, Einstein wrote to Schwarzschild on this result:
Schwarzschild's second paper, which gives what is now known as the "Inner Schwarzschild solution" (in German: "innere Schwarzschild-Lösung"), is valid within a sphere of homogeneous and isotropic distributed molecules within a shell of radius r=R. It is applicable to solids; incompressible fluids; the sun and stars viewed as a quasi-isotropic heated gas; and any homogeneous and isotropic distributed gas.
Schwarzschild's first (spherically symmetric) solution ''does not'' contain a coordinate
singularity on a surface that is now named after him. In his coordinates, this singularity lies on the sphere of points at a particular radius, called the
Schwarzschild radius
The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic ...
:
:
where ''G'' is the
gravitational constant
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
, ''M'' is the mass of the central body, and ''c'' is the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in a vacuum.
[Landau 1975.] In cases where the radius of the central body is less than the Schwarzschild radius,
represents the radius within which all massive bodies, and even
photons
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alway ...
, must inevitably fall into the central body (ignoring
quantum tunnelling
Quantum tunnelling, also known as tunneling ( US) is a quantum mechanical phenomenon whereby a wavefunction can propagate through a potential barrier.
The transmission through the barrier can be finite and depends exponentially on the barrier h ...
effects near the boundary). When the mass density of this central body exceeds a particular limit, it triggers a gravitational collapse which, if it occurs with spherical symmetry, produces what is known as a Schwarzschild
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
. This occurs, for example, when the mass of a
neutron star
A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. white ...
exceeds the
Tolman–Oppenheimer–Volkoff limit The Tolman–Oppenheimer–Volkoff limit (or TOV limit) is an upper bound to the mass of cold, nonrotating neutron stars, analogous to the Chandrasekhar limit for white dwarf stars. If the mass of the said star reaches the limit it will collapse to ...
(about three solar masses).
Cultural references
Karl Schwarzschild appears as a character in the science fiction short story "Schwarzschild Radius" (1987) by
Connie Willis
Constance Elaine Trimmer Willis (born December 31, 1945), commonly known as Connie Willis, is an American science fiction and fantasy writer. She has won eleven Hugo Awards and seven Nebula Awards for particular works—more major SF awards than ...
.
Schwarzschild's Cat is a comic o
XKCD.comcomparing the size and cuteness of cats.
Karl Schwarzchild appears as a character in the story “Schwarzchild’s Singularity” in the collection "When We Cease to Understand the World" (2020) by
Benjamín Labatut
Benjamín Labatut (born 1980) is a Chilean writer.
Early life
Labatut was born in Rotterdam, Netherlands. He spent his childhood in The Hague, Buenos Aires, and Lima. He moved to Santiago, at the age of 14.
Writing
Labatut's first book of st ...
.
Works
The scientific estate of Karl Schwarzschild is stored in a special collection of th
Lower Saxony National- and University Library of Göttingen
;Relativity
* ''
Über das Gravitationsfeld eines Massenpunktes nach der Einstein’schen Theorie.'' Reimer, Berlin 1916, S. 189 ff. (Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften; 1916)
* ''Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit.'' Reimer, Berlin 1916, S. 424-434 (Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften; 1916)
;Other papers
* ''Untersuchungen zur geometrischen Optik I. Einleitung in die Fehlertheorie optischer Instrumente auf Grund des Eikonalbegriffs'', 1906
Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 4 Nummero 1, S. 1-31
* ''Untersuchungen zur geometrischen Optik II. Theorie der Spiegelteleskope'', 1906
Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 4 Nummero 2, S. 1-28
* ''Untersuchungen zur geometrischen Optik III. Über die astrophotographischen Objektive'', 1906
Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 4 Nummero 3, S. 1-54
*
Über Differenzformeln zur Durchrechnung optischer Systeme'
1907, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen S. 551-570
* ''Aktinometrie der Sterne der B. D. bis zur Größe 7.5 in der Zone 0° bis +20° Deklination. Teil A. Unter Mitwirkung von Br. Meyermann, A. Kohlschütter und O. Birck'', 1910
Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 6 Numero 6, S. 1-117
*
Über das Gleichgewicht der Sonnenatmosphäre'
1906, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen S. 41-53
*
Die Beugung und Polarisation des Lichts durch einen Spalt. I.', 1902, Mathematische Annalen
Band 55 S. 177-247
*
Zur Elektrodynamik. I. Zwei Formen des Princips der Action in der Elektronentheorie'
1903, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen S. 126-131
*
Zur Elektrodynamik. II. Die elementare elektrodynamische Kraft'
1903, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen S. 132-141
*
Zur Elektrodynamik. III. Ueber die Bewegung des Elektrons'
1903, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen S. 245-278
*
Ueber die Eigenbewegungen der Fixsterne'
1907, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen S. 614-632
*
Ueber die Bestimmung von Vertex und Apex nach der Ellipsoidhypothese aus einer geringeren Anzahl beobachteter Eigenbewegungen'
1908, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen S. 191-200
* K. Schwarzschild, E. Kron:
Ueber die Helligkeitsverteilung im Schweif des Halley´schen Kometen'
1911, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen S. 197-208
*
Die naturwissenschaftlichen Ergebnisse und Ziele der neueren Mechanik.', 1904
Jahresbericht der Deutschen Mathematiker-Vereinigung, Band 13 S. 145-156
*
Über die astronomische Ausbildung der Lehramtskandidaten.', 1907
Jahresbericht der Deutschen Mathematiker-Vereinigung, Band 16 S. 519-522
;English translations
* ''On the Gravitational Field of a Point-Mass, According to Einstein's Theory''
The Abraham Zelmanov Journal, 2008, Volume 1, P. 10-19* ''On the Gravitational Field of a Sphere of Incompressible Liquid, According to Einstein's Theory''
The Abraham Zelmanov Journal, 2008, Volume 1, P. 20-32* ''On the Permissible Numerical Value of the Curvature of Space''
The Abraham Zelmanov Journal, Volume 1, 2008, pp. 64-73
See also
*
List of things named after Karl Schwarzschild {{Short description, none
Things named after the astronomy and general relativity, relativity scientist Karl Schwarzschild (1873–1916) include:
* Institutions:
** Karl Schwarzschild Medal
** Karl Schwarzschild Observatory
* Astronomical features:
...
References
External links
*
* Roberto B. Salgad
The Light Cone: The Schwarzschild Black HoleObituary in the Astrophysical Journal written by
Ejnar Hertzsprung
Ejnar Hertzsprung (; Copenhagen, 8 October 1873 – 21 October 1967, Roskilde) was a Danish chemist and astronomer.
Career
Hertzsprung was born in Frederiksberg, Denmark, the son of Severin and Henriette. He studied chemical engineering at Cop ...
*
Biography of Karl Schwarzschild by Indranu Suhendro, ''The Abraham Zelmanov Journal'', 2008, Volume 1.
{{DEFAULTSORT:Schwarzschild, Karl
1873 births
1916 deaths
Jewish astronomers
19th-century German astronomers
German relativity theorists
German Ashkenazi Jews
Jewish physicists
Ludwig Maximilian University of Munich alumni
Members of the Prussian Academy of Sciences
Scientists from Frankfurt
People from Hesse-Nassau
University of Strasbourg alumni
University of Göttingen faculty
German Jewish military personnel of World War I
20th-century German astronomers
Deaths from autoimmune disease
German military personnel killed in World War I