Karl Schwarzschild (; 9 October 1873 – 11 May 1916) was a German physicist and astronomer.
Schwarzschild provided 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 a derivation of the Schwarzschild radius, which is the size of the event horizon of a non-rotating black hole.
Schwarzschild accomplished this while serving in the German army during World War I. He died the following year, possibly from the autoimmune disease pemphigus, which he developed while at the Russian front.
Asteroid 837 Schwarzschilda is named in his honour, as is the large crater Schwarzschild, on the far side of the Moon.
Life
Karl Schwarzschild was born on 9 October 1873 in Frankfurt am Main, the eldest of six boys and one girl, to Jewish parents. His father was active in the business community of the city, and the family had ancestors in Frankfurt from the sixteenth century onwards. The family owned two fabric stores in Frankfurt. His brother Alfred became a painter. The young Schwarzschild attended a Jewish primary school until 11 years of age and then the Lessing-Gymnasium (secondary school). He received an all-encompassing education, including subjects like Latin, Ancient Greek, music and art, but developed a special interest in astronomy early on. He proved to be a child prodigy, having two papers on binary orbits (celestial mechanics) published before the age of sixteen.
After graduation in 1890, he attended the University of Strasbourg to study astronomy. After two years he transferred to the Ludwig-Maximilians-Universität München, where he obtained his doctorate in 1896 for a work on Henri Poincaré's theories.
From 1897, he worked as assistant at the Kuffner Observatory in Vienna. His work here concentrated on the photometry of star clusters and laid the foundations for a formula linking the intensity of the starlight, exposure time, and the resulting contrast on a photographic plate. An integral part of that theory is the Schwarzschild exponent (astrophotography). In 1899, he returned to Munich to complete his Habilitation.
From 1901 until 1909, he was a professor at the prestigious Göttingen Observatory within the University of 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. He married Else Rosenbach, a great-granddaughter of Friedrich Wöhler and daughter of a professor of surgery at Göttingen, in 1909. Later that year they moved to Potsdam, where he took up the post of director of the Astrophysical Observatory of Potsdam. This was then the most prestigious post available for an astronomer in Germany.
alt=Schwarzschild, third from left in the automobile; possibly during the Fifth Conference of the International Union for Co-operation in Solar Research, held in Bonn, Germany|thumb|Schwarzschild, third from left in the automobile; possibly during the Fifth Conference of the International Union for Co-operation in Solar Research, held in [[Bonn, Germany]]
thumb|Schwarzschild at the Fourth Conference International Union for Cooperation in Solar Research at [[Mount Wilson Observatory, 1910]]
From 1912, Schwarzschild was a member of the Prussian Academy of Sciences.
Work on general relativity and death
At the outbreak of World War I in 1914, Schwarzschild volunteered for service in the German army despite being over 40 years old. He served on both the western and eastern fronts, specifically helping with ballistic calculations and rising to the rank of second lieutenant in the artillery.
Nevertheless, he managed to write three important papers, two on the theory of relativity 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. He also identified the Schwarzschild radius, at which a star will form what is now known as a black hole, though he wrongly believed this finding to be a mathematical curiosity that had no practical relevance. Twenty-three years after Schwarzschild's death, J. Robert Oppenheimer and Hartland Snyder correctly predicted the existence of black holes in their Oppenheimer–Snyder model, though they did not draw directly on Schwarzschild's work.
thumb|Karl Schwarzschild's grave at [[Stadtfriedhof (Göttingen) ]]Schwarzschild died of immune complications related to his illness on 11 May 1916, at the age of 42.
- Martin Schwarzschild (1912–1997) became a professor of astronomy at Princeton University, and was the first astronomer to lift a telescope into the stratosphere by balloon.
- Alfred Schwarzschild (1914–1944) remained in Nazi Germany and was murdered during the Holocaust.
Work
Schwarzschild's solutions to the Einstein field equations are fundamental to the study of gravitation, as fundamental as Coulomb's law is for electricity. In addition, his research interests were extremely broad, including work in celestial mechanics, observational stellar photometry, quantum mechanics, instrumental astronomy, stellar structure, radiative transfer, stellar statistics, Halley's Comet, and spectroscopy.
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, now known as the Schwarzschild law, 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:
:<math>i = f ( I \,t^p )</math>
(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.
Electrodynamics
According to Wolfgang Pauli, Schwarzschild is the first to introduce the correct Lagrangian formalism of the electromagnetic field as
:<math> S = \frac12 \int (H^2-E^2) \mathrm dV + \int \rho(\phi - \mathbf{A} \cdot \mathbf{u}) \mathrm dV </math>
where <math> \mathbf{E},\mathbf{H} </math> are the electric and applied magnetic fields, <math>\mathbf{A}</math> is the vector potential and <math>\phi</math> 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
:<math>
S=\sum_{i}m_{i}\int_{C_{i\mathrm ds_{i}+\frac{1}{2}\sum_{i,j}\iint_{C_{i},C_{jq_{i}q_{j}\delta\left(\left\Vert P_{i}P_{j}\right\Vert \right)\mathrm d\mathbf{s}_{i}\mathrm d\mathbf{s}_{j}
</math>
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 Hugo Tetrode
and Adriaan Fokker in the 1920s and John Archibald Wheeler and Richard Feynman in the 1940s and constitutes an alternative but equivalent formulation of electrodynamics.
Thermal radiation
In 1906, Schwarzschild developed the concept of radiative equilibrium between convection inside the Sun and thermal radiation at the surface. He developed an equation for radiative transfer and proved that, in accordance to data, the Sun’s photosphere is in radiative equilibrium.
Relativity
thumb|250px|The [[Kepler problem in general relativity, using 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 produced only an approximate solution. In 1916, Einstein wrote to Schwarzschild on this result: