In 1925 Einstein was working on the problem of motion in General Relativity, and also in the early days of his work on unified field theory. Here, Einstein has used a mostly empty page for the purposes of recording his own research notes, which came to from the essence of his 1927 paper "Über die formale Beziehung des Riemannschen Krümmungstensors zu den Feldgleichungen der Gravitation" (Mathematische Annalen. 97, pp. 99-103). This paper appeared in a special issue of Mathematische Annalen, honoring the centenary of the birth of the mathematician Bernhard Riemann. Riemann's work was, of course, essential to the development of General Relativity, and the article discusses the role of the Riemann tensor in physics in determining the gravitational field.
The present notes were made in the same year as Einstein's pioneering “Einheitliche Feldtheorie von Gravitation und Elektrizitat”—his “first truly deep immersion” in unified field theory—was published. In the material offered here, Einstein utilizes the field equations of General Relativity and introduces a new tensor — Rim - R/4gim — which he considers of deeper significance for the law of gravitation. Einstein shows that the anti-symmetric component of the Riemannian curvature tensor will vanish when the tensor Rim - R/4gim vanishes. Einstein then proceeds to construct from the electromagnetic tensor a new energy tensor whose symmetry properties are the same as the Riemannian curvature tensor — thus producing an “electromagnetically enhanced curvature tensor” (in Einstein’s words here).
Atop the recto of this manuscript, Einstein has composed a letter to the Union of Jewish Student Societies in Germany, in which he indicates: “I will always do whatever is possible in order to promote your goals.” Einstein, however, excuses himself from attending their current conference in person due to “urgent work” (later rephrased to “urgent matters”).
Sotheby's would like to thank Dan Kennefick and Diana K. Buchwald of Caltech for their assistance with cataloguing of this manuscript.
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