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| |name = Karl Schwarzschild
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| |image = Schwarzschild.jpg
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| |image_size = 150px
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| |caption = Karl Schwarzschild (1873-1916)
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| |birth_date = {{birth date|1873|10|9}}
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| |birth_place = [[Frankfurt am Main]]
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| |death_date = {{death date and age|1916|5|11|1873|10|9}}
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| |death_place = [[Potsdam]]
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| |nationality = [[Germany|German]]
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| |field = [[Physics]]<br>[[Astronomy]]
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| |work_institutions =
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| |alma_mater = [[Ludwig Maximilian University of Munich]]
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| |doctoral_advisor = [[Hugo von Seeliger]]
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| |doctoral_students =
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| |known_for =
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| |influences =
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| |influenced = [[Martin Schwarzschild]]
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| |prizes =
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| |religion =
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| |footnotes =
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| |signature =
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| }}
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| '''Karl Schwarzschild''' (/'shvarts shĭld/) (October 9, 1873 – May 11, 1916) was a [[Germany|German]] [[physicist]]. He is also the father of [[astrophysicist]] [[Martin Schwarzschild]].
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| He is best known for providing the first exact solution to the [[Einstein field equations]] of [[general relativity]], 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 [[Deriving the Schwarzschild solution|Schwarzschild solution]], which makes use of [[Schwarzschild coordinates]] and the [[Schwarzschild metric]], leads to the well-known [[Schwarzschild radius]], which is the size of the [[event horizon]] of a non-rotating [[black hole]].
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| Schwarzschild accomplished this triumph while serving in the German army during [[World War I]]. He died the following year from [[pemphigus]], a painful [[Autoimmunity|autoimmune disease]] which he developed while at the [[Eastern Front (World War I)|Russian front]].
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| [[Asteroid]] [[837 Schwarzschilda]] is named in his honor.
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| ==Life==
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| Schwarzschild was born in [[Frankfurt am Main]] to [[Jewish]] parents. His father was active in the business community of the city, and the family had ancestors in the city dating back to the sixteenth century.<ref>Sadri Hassani [http://books.google.co.uk/books?id=BCMLOp6DyFIC&pg=PA919&lpg=PA919&dq=Karl+Schwarzschild+Jewish+primary+school&source=bl&ots=fYSafLsRth&sig=-lQzMooeKWWRomBiNMMfGJ_ohHY&hl=en&sa=X&ei=vo7CT76DGJOv8QOp7MzxCg&sqi=2&ved=0CF4Q6AEwBg#v=onepage&q=Karl%20Schwarzschild%20Jewish%20primary%20school&f=false Mathematical Physics: A Modern Introduction to Its Foundations] Retrieved 2012-05-27</ref> Karl attended a Jewish primary school until 11 years of age.<ref name="J J O'Connor and E F Robertson">MacTutor History of Mathematics{{cite web |title=Biography |authorlink=J J O'Connor and E F Robertson|url=http://www-history.mcs.st-and.ac.uk/Biographies/Schwarzschild.html|}} Retrieved 2012-05-27</ref> He was something of a child prodigy, having two papers on binary orbits ([[celestial mechanics]]) published before he was sixteen.<ref>John Daintith - [http://books.google.co.uk/books?id=vqTNfnKJVPAC&pg=PA684&dq=Karl+Schwarzschild+childhood&hl=en&sa=X&ei=35DCT4DdNZP38QOv8KDNCg&ved=0CEkQ6AEwBA#v=onepage&q=Karl%20Schwarzschild%20childhood&f=false Biographical Encyclopedia of Scientists] CRC Press, 18 Aug 2008 Retrieved 2012-05-27</ref><ref>[http://www.google.co.uk/#hl=en&rlz=1W1ADRA_enGB450&sa=X&ei=epHCT4mkOoeA8gP13rmGCw&ved=0CAQQBSgA&q=Karl+Schwarzschild+published+two+papers+on+binary+orbits+by+time+sixteen&spell=1&bav=on.2,or.r_gc.r_pw.r_qf.,cf.osb&fp=696f04903ec9d5bc&biw=1280&bih=897 Search engine verification of : "published papers before sixteen years of age"] Retrieved 2012-05-27</ref> He studied at [[University of Strasbourg|Straßburg]] and [[Ludwig Maximilian University of Munich|Munich]], obtaining his doctorate in 1896 for a work on [[Henri Poincaré]]'s theories.
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| From 1897, he worked as assistant at the [[Kuffner observatory]] in Vienna.
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| From 1901 until 1909 he was a professor at the prestigious institute at [[Göttingen]], where he had the opportunity to work with some significant figures including [[David Hilbert]] and [[Hermann Minkowski]]. Schwarzschild became the director of the [[Göttingen Observatory|observatory in Göttingen]]. He married Else Posenbach, the daughter of a professor of surgery at Göttingen, in 1909, and later that year moved to [[Potsdam]], 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. He and Else had three children, Agathe, Martin (who went on to become a professor of astronomy at Princeton University), and Alfred.
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| From 1912, Schwarzschild was a member of the [[Prussian Academy of Sciences]].
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| At the outbreak of [[World War I]] in 1914 he joined the German army despite being over 40 years old. He served on both the western and eastern fronts, rising to the rank of lieutenant in the artillery.
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| While serving on the front in Russia in 1915, he began to suffer from a rare and painful skin disease called [[pemphigus]]. Nevertheless, he managed to write three outstanding papers, two on [[relativity theory]] and one on [[Quantum mechanics|quantum theory]]. His papers on relativity produced the first exact solutions to the [[Einstein field equations]], and a minor modification of these results gives the well-known solution that now bears his name: the [[Schwarzschild metric]].
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| Schwarzschild's struggle with [[pemphigus]] may have eventually led to his death. He died on May 11, 1916.
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| ==Work==
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| Thousands of dissertations, articles, and books have since been devoted to the study of Schwarzschild's solutions to the [[Einstein field equations]]. However, although Schwarzschild's best known work lies in the area of [[general relativity]], his research interests were extremely broad, including work in [[celestial mechanics]], observational stellar [[photometry (astronomy)|photometry]], [[quantum mechanics]], instrumental [[astronomy]], stellar structure, stellar [[statistics]], [[Halley's comet]], and [[spectroscopy]].<ref name="Eisenstaedt, 1989">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.</ref>
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| Some of his particular achievements include measurements of [[variable star]]s, using photography, and the improvement of optical systems, through the perturbative investigation of geometrical aberrations.
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| ===Physics of photography===
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| While at Vienna in 1897, Schwarzschild developed a formula to calculate the optical density of photographic material. It involved an exponent now known as the [[Schwarzschild exponent]], which is the <math>p</math> in the formula:
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| <math>i = f ( I\cdot t^p )</math>
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| (where <math>i</math> is optical density of exposed photographic emulsion, a function of <math>I</math>, the intensity of the source being observed, and <math>t</math>, the exposure time, with <math>p</math> a constant). This formula was important for enabling more accurate photographic measurements of the intensities of faint astronomical sources.
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| ===Electrodynamics===
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| According to [[Wolfgang Pauli]] (Theory of relativity), Schwarzschild is the first to introduce the correct [[Lagrangian]] formalism of the electromagnetic field <ref name= "schwarzschil1903">K. Schwarzschild, Nachr. ges. Wiss. Gottingen (1903) 125</ref> as
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| <math> S = (1/2) \int (H^2-E^2) dV + \int \rho(\phi - \vec{A}\vec{u}) dV </math>
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| where <math> \vec{E},\vec{H} </math> are the electric and magnetic field, <math>\vec{A}</math> is the vector potential and <math>\phi</math> is the electric potential.
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| 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 <ref name= "schwarzschil1903b">K. Schwarzschild, Nachr. ges. Wiss. Gottingen (1903) 128,132</ref>
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| <math>
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| S=\sum_{i}m_{i}\int_{C_{i}}ds_{i}+\frac{1}{2}\sum_{i,j}\int\int_{C_{i},C_{j}}q_{i}q_{j}\delta\left(\left\Vert P_{i}P_{j}\right\Vert \right)d\mathbf{s}_{i}d\mathbf{s}_{j}
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| </math>
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| where <math> C_\alpha </math> are the world lines of the particle, <math> d\mathbf{s}_{\alpha} </math> 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 <math> \delta\left(\left\Vert P_{i}P_{j}\right\Vert \right) </math>. The idea was further developed by Tetrod and FokKer in the 1920s and Wheeler and Feyman in the 1940s <ref>Wheeler & Feyman, Rev.Mod. Phys. 21:425 (1949)</ref> and constitutes an alternative/equivalent formulation of electrodynamics.
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| ===Relativity===
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| [[Image:Schwarzschild circular radii.svg|thumb|250px|The [[Kepler problem]] in general relativity, using the [[Schwarzschild metric]]]]
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| {{main|Deriving the Schwarzschild solution}}
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| Einstein himself was pleasantly surprised to learn that the [[Einstein field equations|field equations]] admitted exact solutions, because of their prima facie complexity, and because he himself had only produced 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 Schwarzschild was serving in the war stationed on the Russian front. Schwarzschild 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."<ref>Letter from K Schwarzschild to A Einstein dated 22 December 1915, in "The Collected Papers of Albert Einstein", vol.8a, doc.#169, [http://www.gsjournal.net/old/eeuro/vankov.pdf (Transcript of Schwarzschild's letter to Einstein of 22 Dec. 1915)].</ref> In 1916, Einstein wrote to Schwarzschild on this result:
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| {{Quote|I have read your paper with the utmost interest. I had not expected that one could formulate the exact solution of the problem in such a simple way. I liked very much your mathematical treatment of the subject. Next Thursday I shall present the work to the Academy with a few words of explanation.|[[Albert Einstein]]|<ref name="Eisenstaedt, 1989"/>}}
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| [[Image:Schwarzschild interior.jpg|thumb|250px|Boundary region of Schwarzschild interior and exterior solution]]
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| 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.
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| Schwarzschild's first (spherically symmetric) solution contains a coordinate [[Mathematical singularity|singularity]] on a surface that is now named after him. In Schwarzschild coordinates, this singularity lies on the sphere of points at a particular radius, called the [[Schwarzschild radius]]:
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| :<math>
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| R_{s} = \frac{2GM}{c^{2}}
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| </math> | |
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| where ''G'' is the [[gravitational constant]], ''M'' is the mass of the central body, and ''c'' is the [[speed of light]] in a vacuum.<ref name="landau_1975" >Landau 1975.</ref> In cases where the radius of the central body is less than the Schwarzschild radius, <math>R_{s}</math> represents the radius within which all massive bodies, and even [[photons]], must inevitably fall into the central body (ignoring [[quantum tunnelling]] 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]]. This occurs, for example, when the mass of a [[neutron star]] exceeds the [[Tolman-Oppenheimer-Volkoff limit]] (about three solar masses).
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| ==See also==
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| * [[Schwarzschild (disambiguation)]], items named after Karl Schwarzschild
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| * [[Martin Schwarzschild]], son of Karl Schwarzschild, and renowned astronomer
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| ==Works==
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| {{Wikisourcelang|de|Karl Schwarzschild|Works by Karl Schwarzschild}}
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| ;Relativity | |
| * ''[[s:de:Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie|Über das Gravitationsfeld eines Massenpunktes nach der Einstein’schen Theorie.]]'' Reimer, Berlin 1916, S. 189 ff. (Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften; 1916)
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| * ''Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit.'' Reimer, Berlin 1916, S. 424-434 (Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften; 1916)
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| ;Other papers
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| * ''Untersuchungen zur geometrischen Optik I. Einleitung in die Fehlertheorie optischer Instrumente auf Grund des Eikonalbegriffs'', 1906, [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN251726223_0004 Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 4], Nummero 1, S. 1-31
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| * ''Untersuchungen zur geometrischen Optik II. Theorie der Spiegelteleskope'', 1906, [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN251726223_0004 Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 4], Nummero 2, S. 1-28
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| * ''Untersuchungen zur geometrischen Optik III. Über die astrophotographischen Objektive'', 1906, [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN251726223_0004 Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 4], Nummero 3, S. 1-54
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D58230 Über Differenzformeln zur Durchrechnung optischer Systeme]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN252457811_1907 1907, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen], S. 551-570
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| * ''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, [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN251726223_0006 Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Band 6], Numero 6, S. 1-117
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D58114 Über das Gleichgewicht der Sonnenatmosphäre]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN252457811_1906 1906, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen], S. 41-53
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D36450 Die Beugung und Polarisation des Lichts durch einen Spalt. I.]'', 1902, Mathematische Annalen, [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN235181684_0055 Band 55], S. 177-247
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D57298 Zur Elektrodynamik. I. Zwei Formen des Princips der Action in der Elektronentheorie]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN252457811_1903 1903, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen], S. 126-131
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D57299 Zur Elektrodynamik. II. Die elementare elektrodynamische Kraft]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN252457811_1903 1903, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen], S. 132-141
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D57299 Zur Elektrodynamik. III. Ueber die Bewegung des Elektrons]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN252457811_1903 1903, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen], S. 245-278
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D58241 Ueber die Eigenbewegungen der Fixsterne]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN252457811_1907 1907, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen], S. 614-632
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D62941 Ueber die Bestimmung von Vertex und Apex nach der Ellipsoidhypothese aus einer geringeren Anzahl beobachteter Eigenbewegungen]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN252457811_1908 1908, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen], S. 191-200
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| * K. Schwarzschild, E. Kron: ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D63058 Ueber die Helligkeitsverteilung im Schweif des Halley´schen Kometen]'', [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN252457811_1911 1911, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen], S. 197-208
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D244900 Die naturwissenschaftlichen Ergebnisse und Ziele der neueren Mechanik.]'', 1904, [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN37721857X_0013 Jahresbericht der Deutschen Mathematiker-Vereinigung, Band 13], S. 145-156
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| * ''[http://dz-srv1.sub.uni-goettingen.de/contentserver/contentserver?command=docconvert&docid=D244507 Über die astronomische Ausbildung der Lehramtskandidaten.]'', 1907, [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN37721857X_0016 Jahresbericht der Deutschen Mathematiker-Vereinigung, Band 16], S. 519-522
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| ;English translations
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| * ''On the Gravitational Field of a Point-Mass, According to Einstein's Theory'', [http://zelmanov.ptep-online.com/html/zj-2008-03.html The Abraham Zelmanov Journal, 2008, Volume 1, P. 10-19]
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| * ''On the Gravitational Field of a Sphere of Incompressible Liquid, According to Einstein's Theory'', [http://zelmanov.ptep-online.com/html/zj-2008-04.html The Abraham Zelmanov Journal, 2008, Volume 1, P. 20-32]
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| * ''On the Permissible Numerical Value of the Curvature of Space'', [http://zelmanov.ptep-online.com/html/zj-2008-06.html The Abraham Zelmanov Journal, 2008, Volume 1, P. 64-73]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| {{commons category}}
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| * {{MacTutor Biography|id=Schwarzschild}}
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| * Roberto B. Salgado [http://www.phy.syr.edu/courses/modules/LIGHTCONE/schwarzschild.html The Light Cone: The Schwarzschild Black Hole]
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| * [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1917ApJ....45..285H Obituary in the Astrophysical Journal], written by [[Ejnar Hertzsprung]]
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| * {{MathGenealogy|id=52349}}
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| {{Authority control|VIAF=22226062}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Schwarzschild, Karl
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = German astronomer
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| | DATE OF BIRTH = 1873-10-09
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| | PLACE OF BIRTH = [[Frankfurt am Main]]
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| | DATE OF DEATH = 1916-05-11
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| | PLACE OF DEATH = [[Potsdam]]
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| }}
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| {{DEFAULTSORT:Schwarzschild, Karl}}
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| [[Category:1873 births]]
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| [[Category:1916 deaths]]
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| [[Category:German astronomers]]
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| [[Category:German physicists]]
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| [[Category:German Jews]]
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| [[Category:Jewish scientists]]
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| [[Category:Members of the Prussian Academy of Sciences]]
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| [[Category:People from Frankfurt]]
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| [[Category:People from Hesse-Nassau]]
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| [[Category:Relativists]]
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| [[Category:University of Strasbourg alumni]]
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| [[Category:Ludwig Maximilian University of Munich alumni]]
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| [[Category:University of Göttingen faculty]]
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