There are many interesting letters found in The Collected Papers of Albert Einstein. Among those between two physicists are the exchanges between Einstein and Bohr on quantum physics, in which the two titans battle over the interpretation of the Uncertainty Principle. However, to me, one of the most dramatic letters between Einstein and another physicist was an exchange between Einstein and the scientist Karl Schwarzschild on a closed solution to the equations of General Relativity on December 22, 1915. While fighting for the German army on the Russian front, Schwarzschild was able to calculate the gravitational field surrounding an object in space. He also gave a rigorous proof of Einstein’s explanation of the advanced of the perihelion of planet Mercury. A translation of that letter, given below, is taken from Volume 8 of The Collected Papers of Albert Einstein:
As you see, the war has permitted me to escape somewhat into your splendid ideas. I have read your new papers with the utmost interest. I do not know whether you are already familiar with the results I have obtained, so I take the liberty of communicating them to you.
The solution I have found for your equations is indeed the simplest case—namely, the field of a point mass at rest, exhibiting spherical symmetry. It turns out that the equations can be integrated completely in this special case. What is especially pleasing is that the solution satisfies all the criteria for physical acceptability.
In order to express the solution in the form compatible with your coordinate conditions, I had to make use of a somewhat unusual choice of variables. I hope this will not present any difficulty.
I am enclosing a brief manuscript that gives the detailed form of the metric and shows that it satisfies the field equations.
I was very happy to be able to make this contribution—even from out here, in this outpost of culture and science.
With best regards and wishes for continued success in your great endeavors,
Yours most respectfully,Karl Schwarzschild
Einstein responded on January, 13, 1916 in the letter translated below.
Dear Colleague,
I have read your paper with the utmost interest. I had not expected that the exact solution to the problem could be formulated so simply. I liked your formulation very much.
The only thing that troubles me is the fact that your solution has a singularity at the origin (r = 0), but perhaps that is inevitable.
I consider it a great achievement that, in spite of your military duties, you have succeeded in dealing with such difficult problems so successfully.
With cordial greetings and sincere thanks,
Yours,
A. Einstein
A few weeks later, Schwarzschild sent Einstein another letter indicating that the mathematical equations for gravitational forces inside a star have a singularity as the radius of the star shrinks beyond a certain value. That is, the star collapses into a dense mass of such great gravitational attraction that no radiation nor light can escape from it and it becomes, what we now call “a black hole.”
A few months after sending his two letters, Schwarzschild died of pemphigus, an autoimmune disease that attacks the skin. He never lived to see the celebration and acceptance of the General Theory of Relativity.
