Die Poincarésche Theorie des Gleichgewichts einer Homogenen Rotierenden Flüssigkeitsmasse.

the predictor of black holes

First edition, the offprint of Karl Schwarzschild's doctoral thesis on Poincairé's theory of the equilibrium of a homogeneous rotating fluid mass. Rare, with no copies conclusively located by WorldCat (unless the British Library copy dated 1898 is simply misdated) and none in auction records. This copy from the library of Magnus F. Fischer, who may have been an astronomer, as the bookplate depicts an observatory.

Karl Schwarzschild (1873-1916) is one of the most remarkable and tragic figures in 20th century physics. After completing this dissertation he worked on the photometry of solar clusters at the Kuffner observatory in Vienna, establishing the mathematical relationship between a star's intensity and its contrast on a photographic plate. During the first decade of the 20th century he worked at Göttingen University Observatory, associating with cutting-edge mathematicians such as David Hilbert and Hermann Minkowski. In 1909 he obtained the prestigious post of director of the Astronomical Observatory at Potsdam, but enlisted when war was declared.

While at the front, Schwarzschild 'received an issue of the Sitzungsberichte (Proceedings) of the Berlin Academy of Sciences, containing a paper by Albert Einstein, arguing that gravity is merely the result of the curvature of space-time. This paper set forth the general theory of relativity, a follow-up to the special theory of 1905. In the 1915 paper, Einstein wrote down, using metrics, what came to be called his "field equations," which, if solved, would allow one to calculate the forces of gravitation anywhere in space' (Ashworth, Linda Hall Library Scientist of the Day, October 9, 2024). Einstein was able to approximate the solution to the equations, enough to predict the bending of light by gravitational fields. 'Schwarzschild, in 1915, was one of the few who could work with Einstein's metrics, and he decided to see if he could find an exact solution to the field equations by considering a simple case, the curvature of space-time around a point-mass. And he was able to do so, providing the first exact solutions to the equations of general relativity'.

The most remarkable result of Schwarzschild's work was that the equations predicted a singularity - what we now know as a black hole - and he was able to provide the formula for the singularity's radius, the Schwarzschild radius, which delineates the event horizon. Schwarzschild sent two papers on his results to Einstein, who was delighted and had them published immediately. But the author did not live to see this - he died of an autoimmune disease only a few months later, in May of 1916.

First edition, offprint; diagrams within the text, occasional contemporary pencilled notes in the text, hand-drawn diagrams on stiff card loosely inserted, contents toned, mild vertical crease from folding; original blue-grey wrappers printed in black, contemporary wrapper of thick purple paper over the original wrappers, contemporary inscriptions and tickets to the upper wrapper and added wrapper, bookplate, original wrappers partially browned and a bit rubbed and creased, very good condition; 69 pp.