Karl Schwarzschild was a
GermanGermany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
physicistA physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
. He is also the father of astrophysicist
Martin SchwarzschildMartin Schwarzschild was a German American astronomer. He was the son of famed astrophysicist Karl Schwarzschild and the nephew of the Swiss astrophysicist Robert Emden.-Biography:...
.
He is best known for providing the first exact solution to the
Einstein field equationsThe Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
of
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It 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 solutionThe Schwarzschild solution is one of the simplest and most useful solutions of theEinstein field equations . It describes spacetime in the vicinity of a non-rotating massive spherically-symmetric object...
, which makes use of
Schwarzschild coordinatesIn 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 coordinate chart on a static and spherically symmetric...
and the
Schwarzschild metricIn Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...
, leads to the well-known
Schwarzschild radiusThe Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...
, which is the size of the
event horizonIn general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...
of a non-rotating
black holeA black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
.
Schwarzschild accomplished this triumph while serving in the German army during
World War IWorld War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
. He died the following year from
pemphigusPemphigus is a rare group of blistering autoimmune diseases that affect the skin and mucous membranes.In pemphigus, autoantibodies form against desmoglein. Desmoglein forms the "glue" that attaches adjacent epidermal cells via attachment points called desmosomes...
, a painful
autoimmune diseaseAutoimmunity is the failure of an organism to recognize its own constituent parts as self, which allows an immune response against its own cells and tissues. Any disease that results from such an aberrant immune response is termed an autoimmune disease...
which he developed while at the
Russian frontThe Eastern Front was a theatre of war during World War I in Central and, primarily, Eastern Europe. The term is in contrast to the Western Front. Despite the geographical separation, the events in the two theatres strongly influenced each other...
.
AsteroidAsteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
837 Schwarzschilda837 Schwarzschilda is a minor planet orbiting the Sun. it is named after Karl Schwarzschild, a physicist and astronomer who had died earlier that year....
is named in his honour.
Life
Schwarzschild was born in Frankfurt am Main to Jewish parents. He was something of a child prodigy, having a paper on
celestial mechanicsCelestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
published when he was only sixteen. He studied at
StrasbourgStrasbourg is the capital and principal city of the Alsace region in eastern France and is the official seat of the European Parliament. Located close to the border with Germany, it is the capital of the Bas-Rhin département. The city and the region of Alsace are historically German-speaking,...
and
MunichMunich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
, obtaining his doctorate in 1896 for a work on Jules Henri Poincaré's theories.
From 1897, he worked as assistant at the
Kuffner observatoryThe Kuffner observatory is one of two telescope-equipped public 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.
From 1901 until 1909 he was a professor at the prestigious institute at
GöttingenGöttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
, where he had the opportunity to work with some significant figures including
David HilbertDavid Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
and
Hermann MinkowskiHermann Minkowski was a German mathematician of Ashkenazi Jewish descent, who created and developed the geometry of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.- Life and work :Hermann Minkowski was born...
. Schwarzschild became the director of the
observatory in GöttingenGöttingen Observatory is a German astronomical observatory located in Göttingen, Lower Saxony, Germany.-History:...
.
He moved to a post at the Astrophysical Observatory in
PotsdamPotsdam is the capital city of the German federal state of Brandenburg and part of the Berlin/Brandenburg Metropolitan Region. It is situated on the River Havel, southwest of Berlin city centre....
in 1909.
From 1912, Schwarzschild was a member of the
Prussian Academy of SciencesThe Prussian Academy of Sciences was an academy established in Berlin on 11 July 1700, four years after the Akademie der Künste or "Arts Academy", to which "Berlin Academy" may also refer.-Origins:...
.
At the outbreak of
World War IWorld War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
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
pemphigusPemphigus is a rare group of blistering autoimmune diseases that affect the skin and mucous membranes.In pemphigus, autoantibodies form against desmoglein. Desmoglein forms the "glue" that attaches adjacent epidermal cells via attachment points called desmosomes...
. Nevertheless, he managed to write three outstanding papers, two on relativity theory and one on
quantum theoryQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. His papers on relativity produced the first exact solutions to the
Einstein field equationsThe Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
, and a minor modification of these results gives the well-known solution that now bears his name: the
Schwarzschild metricIn Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...
.
Schwarzschild's struggle with
pemphigusPemphigus is a rare group of blistering autoimmune diseases that affect the skin and mucous membranes.In pemphigus, autoantibodies form against desmoglein. Desmoglein forms the "glue" that attaches adjacent epidermal cells via attachment points called desmosomes...
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 equationsThe Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
. However, although Schwarzschild's best known work lies in the area of
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, his research interests were extremely broad, including work in
celestial mechanicsCelestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
, observational stellar
photometryPhotometry is a technique of astronomy concerned with measuring the flux, or intensity of an astronomical object's electromagnetic radiation...
,
quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, instrumental
astronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, stellar structure, stellar
statisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, Halley's comet, and
spectroscopySpectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
.
Some of his particular achievements include measurements of
variable starA star is classified as variable if its apparent magnitude as seen from Earth changes over time, whether the changes are due to variations in the star's actual luminosity, or to variations in the amount of the star's light that is blocked from reaching Earth...
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 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 W. Pauli (Theory of relativity), Schwarzschild is the first to introduce the correct
LagrangianThe Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
formalism of the electromagnetic field as
where
are the electric and magnetic field,
is the vector potential and
is the electric potential.
Relativity
Einstein himself was pleasantly surprised to learn that the
field equationsThe Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
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." 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
singularityIn mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability...
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 radiusThe Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...
:
where
G is the
gravitational constantThe gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
,
M is the mass of the central body, and
c is the
speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
in a vacuum. 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, must inevitably fall into the central body (ignoring
quantum tunnellingQuantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...
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 holeA black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
. This occurs, for example, when the mass of a
neutron starA neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
exceeds the
Tolman-Oppenheimer-Volkoff limitThe Tolman–Oppenheimer–Volkoff limit is an upper bound to the mass of stars composed of neutron-degenerate matter . The TOV limit is analogous to the Chandrasekhar limit for white dwarf stars.-History:...
(about three solar masses).
See also
- Schwarzschild
Schwarzschild is a German surname meaning "black sign" or "black shield" and may refer to:* Henry Schwarzschild, , founder of NCADP, LCDC, and head of ACLU's Capital Punishment project in America...
, items named after Karl Schwarzschild
- Martin Schwarzschild
Martin Schwarzschild was a German American astronomer. He was the son of famed astrophysicist Karl Schwarzschild and the nephew of the Swiss astrophysicist Robert Emden.-Biography:...
, son of Karl Schwarzchild, and renowned astronomer
Works
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, 2008, Volume 1, P. 64-73
External links