# Where did Karl Schwarzschild derived his solution?

Does anyone know more about circumstances of Karl Schwarzschild at the Russian front in 1915 where he allegedly derived his famous solution of the Einstein equations (describing a black hole)? Sources I know only repeat that he served in artillery, but do not mention the exact place where he wrote his letter to Einstein including the solution, or other details.

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Googling for "Einstein-Schwarzschild correspondence" (since the solution first appeared in a letter to Einstein), I came across a valuable source: a new book A New Approach to Differential Geometry Using Clifford's Geometric Algebra by John Snygg. Some relevant pages (unfortunately without pagination) are freely available at Google Books. Snygg writes (in my transcription from the Google Books images):

"In August of 1915, Karl Schwarzschild along with his artillery brigade was assigned to the Tenth Army on the Russian Front at Kovoso in the present day Lithuania [...]".

I have not been able to localize Kovoso by now, but this doesn't matter as you will see:

"According to most biographies of Einstein, Schwarzschild sent his famous solution to Einstein from the Russian front in a letter dated December 22, 1915. However, correspondence with his wife shows that by the end of September he had been relocated to Mulhouse in Alsace. He was then relocated again to someplace else but by December 1, he was back in Mulhouse. Historian Tilman Sauer has drawn my attention to a letter Schwarzschild wrote to Arnold Sommerfeld on the same date that Schwarzschild mailed his solution to Einstein [Schwarzschild 1915]. In the letter to Sommerfeld Schwarzschild describes hearing canon fire from Hartmannweilerkopf, which is about 10 km from Mulhouse."

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Nice story! How did he arrive at his solution? Same way we do it now (as described in many GR books) ? –  magma Nov 14 '12 at 18:57
@magma I don't understand general theory of relativity so I cannot give fully qualified answer to your comment, but I am quite sure that answer is no. First, in 1915 general theory of relativity has not been completed yet. Second, what is in textbooks presented as Schwarzschild solution is not the solution he derived in December 1915. Third, he used different coordinates. By the way, I think it was not realized by physicists until 1960s that an observer can actually reach and pass the Schwarzschild radius and that it presents the point of no return. –  Leos Ondra Nov 14 '12 at 20:47
Schwarzschild could not have found an exact solution to the field equations if he had not known the final (Dec 2 1915) form of the equations. He knew them and he used spherical coordinates to obtain a form closely related to the standard one (en.wikipedia.org/wiki/Karl_Schwarzschild#Relativity ). Lemaitre in 1933 already realized that the Schwarzschild radius is not a phisical singularity (MTW pag 822) –  magma Nov 14 '12 at 23:50
@magma You might be right, as I said I am not expert in this field. I will check details and post them later. –  Leos Ondra Nov 15 '12 at 7:16
@magma I have consulted historical study by Matthias Schemmel (An Astronomical Road to General Relativity: The Continuity between Classical and Relativistic Cosmology in the Work of Karl Schwarzschild, Science in Context 18(3), 451–478, 2005) and he writes 1) that Schwarzschild (on leave from his military duties) attended the meeting of the Prussian Academy of sciences on November 18, 1915 where Einstein presented his theory, and 2) that he used the field equations $G_{\mu \nu} = - \kappa T_{\mu \nu}$ which didn't matter in vacuum. –  Leos Ondra Nov 15 '12 at 18:54