# Karl Schwarzschild

Karl Schwarzschild

Infobox Scientist
name = Karl Schwarzschild
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caption = Karl Schwarzschild (1873-1916)
birth_date = October 9, 1873
birth_place = Frankfurt am Main
death_date = May 11, 1916
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nationality = German
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field = physics astronomy
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influenced = Martin Schwarzschild
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Karl Schwarzschild (October 9, 1873 - May 11, 1916) was a German Jewish physicist and astronomer. He is also the father of astrophysicist Martin Schwarzschild.

He was born in Frankfurt am Main. He was something of a child prodigy, having a paper on celestial mechanics published when he was only sixteen. He studied at Strasbourg and Munich, obtaining his doctorate in 1896 for a work on Jules Henri Poincaré's theories.

From 1897, he worked as assistant at the [http://kuffner-sternwarte.at/sternwarte/vks_ksw.html Kuffner Sternwarte] (Observatory) in Vienna, where he developed a formula to calculate the optical density of photographic material. It involved an exponent now known as the Schwarzschild-exponent, which is the $p$ in the formula:

$i = f \left( Icdot t^p \right)$

(where $i$ is optical density of exposed photographic emulsion, a function of $I$, the intensity of the source being observed, and $t$, the exposure time, with $p$ a constant). This formula was important for enabling more accurate photographic measurements of the intensities of faint astronomical sources.

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 observatory in Göttingen. He moved to a post at the Astrophysical Observatory in Potsdam in 1909.

From 1912, Schwarzschild was a member of the Prussian Academy of Sciences.

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.

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 theory. His papers on relativity produced the first exact solutions to the Einstein field equations, and a minor modifaction of these results gives the well-known solution that now bears his name: the Schwarzschild metric.

Einstein himself was pleasantly surprised to learn that the 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. 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 contains a coordinate 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:

:$R_\left\{s\right\} = frac\left\{2GM\right\}\left\{c^\left\{2$

where "G" is the gravitational constant, "M" is the mass of the central body, and "c" is the speed of light in a vacuum.Landau 1975.] In cases where the radius of the central body is less than the Schwarzschild radius, $R_\left\{s\right\}$ 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 Oppenheimer-Volkoff limit (about three solar masses).

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, quantum mechanics, instrumental astronomy, stellar structure, stellar statistics, Halley's comet, and spectroscopy. [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 stars, using photography, and the improvement of optical systems, through the perturbative investigation of geometrical aberrations.

Schwarzschild's struggle with pemphigus may have eventually led to his death. He died on May 11, 1916.

ee also

* Schwarzschild, items named after Karl Schwarzschild

References

*
* Roberto B. Salgado [http://www.phy.syr.edu/courses/modules/LIGHTCONE/schwarzschild.html The Light Cone: The Schwarzschild Black Hole]
* [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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