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.

Schwarzschild accomplished this while serving in the German army during World War I.

He died the following year from the autoimmune disease pemphigus, which he developed while at the Russian front.

[4][5][6] Asteroid 837 Schwarzschilda is named in his honour, as is the large crater Schwarzschild, on the far side of the Moon.

[7] Karl Schwarzschild was born on 9 October 1873 in Frankfurt on Main, the eldest of six boys and one girl,[8][9] 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.

He received an all-encompassing education, including subjects like Latin, Ancient Greek, music and art, but developed a special interest in astronomy early on.

[13] In fact he was something of a child prodigy, having two papers on binary orbits (celestial mechanics) published before the age of sixteen.

After two years he transferred to the Ludwig Maximilian University of Munich where he obtained his doctorate in 1896 for a work on Henri Poincaré's theories.

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.

He married Else Rosenbach, a great-granddaughter of Friedrich Wöhler and daughter of a professor of surgery at Göttingen, in 1909.

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.

[8] While serving on the front in Russia in 1915, he began to suffer from pemphigus, a rare and painful autoimmune skin-disease.

[17] In March 1916, Schwarzschild left military service because of his illness and returned to 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 the Einstein field equations.

[21] 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.

This formula was important for enabling more accurate photographic measurements of the intensities of faint astronomical sources.

According to Wolfgang Pauli,[22] Schwarzschild is the first to introduce the correct Lagrangian formalism of the electromagnetic field [23] as

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 by Hugo Tetrode[25] and Adriaan Fokker[26] in the 1920s and John Archibald Wheeler and Richard Feynman in the 1940s [27] and constitutes an alternative but equivalent formulation of electrodynamics.

[17] 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.

"[28] In 1916, Einstein wrote to Schwarzschild on this result: I have read your paper with the utmost interest.

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.

Schwarzschild's first (spherically symmetric) solution does not contain a coordinate singularity on a surface that is now named after him.

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.

The entire scientific estate of Karl Schwarzschild is stored in a special collection of the Lower Saxony National- and University Library of Göttingen.