## Näherungsweise Integration der Feldgleichungen der Gravitation [Approximate Integration of the Field Equations of Gravitation]

*”The paper published by Einstein on this linearized approximation [to the field equations of general relativity] in 1916... became the first mathematical theory of gravitational waves, and the approach it pioneered is still fundamental to the design of such existing gravitational wave detectors as the LIGO, VIRGO, and GEO600 detectors operating (respectively) in the United States, Italy, and Germany” -Kennefick, “‘Einstein, gravitational waves, and the theoretician’s regress”.*

RARE FIRST EDITION, COMMERICAL OFFPRINT ISSUE, OF EINSTEIN’S FIRST PROPOSAL OF THE EXISTENCE OF GRAVITATIONAL WAVES.

"Shortly after Einstein published his general theory of relativity, he began wondering how he could use it to solve some of the outstanding problems in physics and astronomy… One of his first applications came in 1916. It was well known that oscillating charges gave rise to electromagnetic waves. Was it possible that the oscillating masses would also give rise to waves? They would be weak because gravity was a weak force, but they should exist.

"Using the equations of general relativity, Einstein looked into the problem and found that gravitational waves should, indeed, exist, and he obtained a formula that described them. He published his results in June 1916, but he wasn't satisfied with his calculation, and after checking it through, he found he had made a mistake. He therefore published a second paper in 1918 correcting the mistake and extending the ideas of his previous paper...

"Einstein found that gravitational waves would be given off by matter when it was accelerated. He considered a rotating rod, but he was disappointed to find that the intensity of the gravitational radiation from it was exceedingly low. He saw that it would take a much more massive system if the waves were to be detected. He therefore considered a binary star system (two stars revolving around one another), but was disappointed again. The mass of the stars would have to be much greater than that of ordinary stars if the radiation was to be detectable. His calculations showed that the stars would have to be exceedingly dense and close together, and at that time no such stars were known. Einstein eventually became convinced that gravitational waves would never be detected" (Parker, *Albert Einstein's Vision*).

Over the years doubts persisted that gravitational waves could be detected, or even existed. This “was the case up until September 14, 2015, when LIGO [Laser Interferometer Gravitational-Wave Observatory], for the first time, physically sensed distortions in spacetime itself caused by passing gravitational waves generated by two colliding black holes nearly 1.3 billion light years away! LIGO and its discovery will go down in history as one of the greatest human scientific achievements,” confirming Einstein’s predictions from a hundred years earlier. (LIGO website).

Commercial offprint from Sitzungsberichte der Königlich preussischen Akademie der Wissenschaften, XXXII, pp. 688-696. Berlin: Königlich Akademie der Wissenschaften, 1916. Octavo (252 x 179 mm), original printed wrappers, custom box. Approx. 5 cm pencil line on front wrapper, very mild creasing to wrappers, otherwise fine. SCARCE, especially in such good condition.

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