Page "Karl Schwarzschild" Paragraph 18

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.

" In 1916, Einstein wrote to Schwarzschild on this result: