Karl Schwarzschild | |
|---|---|
 | |
| Born | (1873-10-09)9 October 1873 |
| Died | 11 May 1916(1916-05-11) (aged 42)[1]: xix Potsdam, German Empire |
| Alma mater | Ludwig Maximilian University of Munich University of Strasbourg |
| Scientific career | |
| Fields | Physics Astronomy |
| Doctoral advisor | Hugo von Seeliger |
| Military career | |
| Allegiance |  German Empire |
| Service | Imperial German Army |
| Years of service | 1914–1916 |
| Rank | Lieutenant |
| Battles / wars | World War I |
Karl Schwarzschild (German:[kaʁlˈʃvaʁtsʃɪlt]ⓘ; 9 October 1873 – 11 May 1916) was a Germanphysicist and astronomer.
Schwarzschild provided the firstexact solution to theEinstein field equations ofgeneral 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. TheSchwarzschild solution, which makes use ofSchwarzschild coordinates and theSchwarzschild metric, leads to a derivation of theSchwarzschild radius, which is the size of theevent horizon of a non-rotatingblack hole.
Schwarzschild accomplished this while serving in the German army duringWorld War I. He died the following year, possibly from theautoimmune diseasepemphigus, which he developed while at theRussian front.[2][3]
Asteroid837 Schwarzschilda is named in his honour, as is the large craterSchwarzschild, on the far side of theMoon.[4]
Karl Schwarzschild was born on 9 October 1873 inFrankfurt on Main, the eldest of six boys and one girl,[5][6] toJewish parents. His father was active in thebusiness community of the city, and the family had ancestors in Frankfurt from the sixteenth century onwards.[7] The family owned two fabric stores in Frankfurt. His brother Alfred became a painter.[8] The young Schwarzschild attended a Jewish primary school until 11 years of age[9] and then theLessing-Gymnasium (secondary school). He received an all-encompassing education, including subjects like Latin, Ancient Greek, music and art, but developed a special interest inastronomy early on.[10] In fact he was something of a child prodigy, having two papers on binary orbits (celestial mechanics) published before the age of sixteen.[11]
After graduation in 1890, he attended theUniversity of Strasbourg to study astronomy. After two years he transferred to theLudwig Maximilian University of Munich where he obtained his doctorate in 1896 for a work onHenri Poincaré's theories.
From 1897, he worked as assistant at theKuffner Observatory in Vienna. His work here concentrated on thephotometry of star clusters and laid the foundations for a formula linking the intensity of the starlight, exposure time, and the resulting contrast on aphotographic plate. An integral part of that theory is theSchwarzschild exponent (astrophotography). In 1899, he returned to Munich to complete hisHabilitation.
From 1901 until 1909, he was a professor at the prestigiousGöttingen Observatory within theUniversity of Göttingen,[12] where he had the opportunity to work with some significant figures, includingDavid Hilbert andHermann Minkowski. Schwarzschild became the director of the observatory. He married Else Rosenbach, a great-granddaughter ofFriedrich Wöhler and daughter of a professor of surgery at Göttingen, in 1909. Later that year they moved toPotsdam, 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.[citation needed]
From 1912, Schwarzschild was a member of thePrussian Academy of Sciences.
At the outbreak ofWorld War I in 1914, Schwarzschild volunteered for service in theGerman army despite being over 40 years old. He served on both the western and eastern fronts, specifically helping withballistic calculations and rising to the rank of second lieutenant in the artillery.[5]
While serving on the front in Russia in 1915, he began to suffer frompemphigus, a rare and painful autoimmune skin-disease.[13] Nevertheless, he managed to write three outstanding papers, two on thetheory of relativity and one onquantum theory. His papers on relativity produced the first exact solutions to theEinstein field equations, and a minor modification of these results gives the well-known solution that now bears his name — theSchwarzschild metric.[14]
In March 1916, Schwarzschild left military service because of his illness and returned toGöttingen. Two months later, on May 11, 1916, his struggle withpemphigus may have led to his death at the age of 42.[13]
He rests in his family grave at theStadtfriedhof Göttingen.
With his wife Else he had three children:
Thousands of dissertations, articles, and books have since been devoted to the study of Schwarzschild's solutions to theEinstein field equations. However, although his best known work lies in the area ofgeneral relativity, his research interests were extremely broad, including work incelestial mechanics, observational stellarphotometry,quantum mechanics, instrumentalastronomy, stellar structure, stellarstatistics,Halley's Comet, andspectroscopy.[18]
Some of his particular achievements include measurements ofvariable stars, using photography, and the improvement of optical systems, through the perturbative investigation of geometrical aberrations.
While at Vienna in 1897, Schwarzschild developed a formula, now known as theSchwarzschild 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.
According toWolfgang Pauli,[19] Schwarzschild is the first to introduce the correctLagrangian formalism of the electromagnetic field[20] 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[21]
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 byHugo Tetrode[22]andAdriaan Fokker[23] in the 1920s andJohn Archibald Wheeler andRichard Feynman in the 1940s[24] and constitutes an alternative but equivalent formulation of electrodynamics.
Einstein himself was pleasantly surprised to learn that thefield equations admitted exact solutions, because of theirprima facie complexity, and because he himself had produced only an approximate solution.[14] 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 is kindly disposed toward me, allowing me, despite fierce gunfire at a decidedly terrestrial distance, to take this walk into this your land of ideas."[25] In 1916, Einstein wrote to Schwarzschild on this result:
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.
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) solutiondoes not contain a coordinatesingularity 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 theSchwarzschild radius:
whereG is thegravitational constant,M is the mass of the central body, andc is thespeed of light in vacuum.[26] In cases where the radius of the central body is less than the Schwarzschild radius, represents the radius within which all massive bodies, and evenphotons, must inevitably fall into the central body (ignoringquantum 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 Schwarzschildblack hole. This occurs, for example, when the mass of aneutron star exceeds theTolman–Oppenheimer–Volkoff limit (about three solar masses).
Karl Schwarzschild appears as a character in the science fiction short story "Schwarzschild Radius" (1987) byConnie Willis.
Karl Schwarzchild appears as a fictionalized character in the story “Schwarzchild’s Singularity” in the collection "When We Cease to Understand the World" (2020) byBenjamín Labatut.
The entire scientific estate of Karl Schwarzschild is stored in a special collection of theLower Saxony National- and University Library of Göttingen.
Relativity
Other papers
English translations
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