Share on Facebook Share on Twitter Email
Answers.com

Karl Schwarzschild

 
Britannica Concise Encyclopedia: Karl Schwarzschild
Home > Library > Miscellaneous > Britannica Concise Encyclopedia

(born Oct. 9, 1873, Frankfurt am Main, Ger. — died May 11, 1916, Potsdam) German astronomer. He published his first paper (on celestial orbits) at age 16. In 1901 he became professor and director of the observatory at the University of Göttingen. He gave the first exact solution of Albert Einstein's general equations of gravitation, which led to a description of how mass curves space. He also laid the foundation of the theory of black holes, using the gravitational equations to show that a body of sufficient mass would have an escape velocity greater than the speed of light and therefore would not be directly observable, since even light rays from it could not escape into space. See also Schwarzschild radius.

For more information on Karl Schwarzschild, visit Britannica.com.

Search unanswered questions...

Enter a question here...
Search: All sources Community Q&A Reference topics

Scientist: Karl Schwarzschild
Top
Home > Library > Science > Dictionary of Scientists

German astronomer (1873–1916)

Schwarzschild was the son of a prosperous Jewish businessman from Frankfurt am Main. His interest in astronomy arose while he was at school and he had published two papers on binary orbits by the time he was 16. Following two years at the University of Strasbourg, he went in 1893 to the University of Munich, obtaining his PhD in 1896. He worked at the Kuffner Observatory in Vienna from 1896 to 1899 and after a period of lecturing and writing became in 1901 associate professor, later professor, at the University of Göttingen and director of its observatory. In 1909 he was appointed director of the Astrophysical Observatory in Potsdam. He volunteered for military service in 1914 at the beginning of World War I and was invalided home in 1916 with a rare skin disease from which he died.

Schwarzschild's practical skill was demonstrated by the instruments he designed, the measuring techniques he devised, and the observations he made. In the 1890s, while the use of photography for scientific purposes was still in its infancy, he developed methods whereby the apparent magnitude, i.e., observed brightness, of stars could be accurately measured from a photographic plate. At that time stellar magnitudes were usually determined by eye. He was then able to establish the photographic magnitude of 3500 stars brighter than magnitude 7.5 and lying between 0° and 20° above the celestial equator. He also determined the magnitude of the same stars visually, demonstrating that the two methods do not yield identical results. This difference between the visual and photographic magnitude of a star, measured at a particular wavelength, is known as its color index.

Schwarzschild also made major contributions to theoretical astronomy, the subjects including orbital mechanics, the curvature of space, and the surface structure of the Sun. In 1906 he published a paper showing that stars could not just be thought of as a gas held together by its own gravity. Questions of thermodynamics arise, concerning the transfer of heat within the star both by radiation and convection, that need a full mathematical treatment.

Einstein's theory of general relativity was published in 1916. While serving in Russia, Schwarzschild wrote two papers on the theory, which were also published in 1916. He gave a solution – the first to be found – of the complex partial differential equations by which the theory is expressed mathematically and introduced the idea of what is now called the Schwarzschild radius. When a star, say, is contracting under the effect of gravity, if it attains a particular radius then the gravitational potential will become infinite. An object will have to travel at the velocity of light to escape from the gravitational field of the star. The value of this radius, the Schwarzschild radius, SR, depends on the mass of the body. If a body reaches a radius less than its SR nothing, including light, will be able to escape from it and it will be what is now known as a ‘black hole’. The SR for the Sun is 3 kilometers while its actual radius is 700,000 kilometers. The theoretical study of black holes and the continuing search for them has become an important field in modern astronomy.

Schwarzchild's son, Martin, also became a noted astronomer.

Wikipedia: Karl Schwarzschild
Top
Home > Library > Miscellaneous > Wikipedia
Karl Schwarzschild

Karl Schwarzschild (1873-1916)
Born October 9, 1873(1873-10-09)
Frankfurt am Main
Died May 11, 1916 (aged 42)
Potsdam
Nationality German
Fields Physics
Astronomy
Alma mater Ludwig Maximilian University of Munich
Doctoral advisor Hugo von Seeliger
Influenced Martin Schwarzschild

Karl Schwarzschild (October 9, 1873 – May 11, 1916) was a German physicist. He is also the father of astrophysicist Martin Schwarzschild.

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 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.

Schwarzschild accomplished this triumph while serving in the German army during World War I. He died the following year from a painful autoimmune disease which he contracted while at the Russian front.

Contents

Life

Schwarzschild 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 Kuffner observatory in Vienna.

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 modification of these results gives the well-known solution that now bears his name: the Schwarzschild metric.

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

Work

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.[1]

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.

Physics of photography

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 p in the formula:

i = f ( I\cdot t^p )

(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.

Electrodynamics

According to W. Pauli (Theory of relativity), Schwarzschild is the first to introduce the correct Lagrangian formalism of the electromagnetic field [2] as

S = (1/2) \int (H^2-E^2) dV + \int \rho(\phi - \vec{A}\vec{u}) dV

where \vec{E},\vec{H} are the electric and magnetic field, \vec{A} is the vector potential and φ is the electric potential.

Relativity

The Kepler problem in general relativity, using the Schwarzschild metric
Main article: Deriving the Schwarzschild solution

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 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."[3] 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.
—Albert Einstein, [1]
Boundary region of Schwarzschild interior and exterior solution

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_{s} = \frac{2GM}{c^{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.[4] In cases where the radius of the central body is less than the Schwarzschild radius, Rs 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).

See also

References

  1. ^ a b 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.
  2. ^ K. Schwarzschild, Nachr. ges. Wiss. Gottingen (1903) 125
  3. ^ 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).
  4. ^ Landau 1975.

External links


This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

 
 
Learn More
Schwarzschild radius (radius of a collapsing celestial object)
Schwarzschild
black hole (in astronomy)

Who was Karl Benz? Read answer...
Who is Karl Kenkins? Read answer...
Who was karl silberbauer? Read answer...

Help us answer these
Who is Karl dowell?
What is french for karl?
Who was Karl Leibnicht?

Post a question - any question - to the WikiAnswers community:

 

Copyrights:

Britannica Concise Encyclopedia. Britannica Concise Encyclopedia. © 2006 Encyclopædia Britannica, Inc. All rights reserved.  Read more
Scientist. A Dictionary of Scientists. Copyright © Market House Books Ltd 1993, 1999, 2003. All rights reserved.  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Karl Schwarzschild".  Read more