Einstein Infeld Hoffmann (3 results)

4to (252 x 174 mm). Pages 65-100 (= 36 pp.). Offprint from the Annals of Mathematics, vol. 39, no. 1. Original printed wrappers, signed "A. Einstein" on upper cover. A signed offprint of Einstein's influential paper on the formulation of gravitational field equations and the motion of bodies. Einstein, with Leopold Infeld and Banesh Hoffmann, here addresses one of the defining technical problems of general relativity and seeks to show how the field equations themselves suffice to determine motion without recourse to separate laws. - The paper marks a critical stage in the maturation of relativistic gravitational theory and stands at the origin of what are now known as the Einstein-Infeld-Hoffmann equations, a seminal result in the approximation of the dynamics of gravitating bodies. Produced in the final decade of Einstein's career, the work belongs to the sustained attempt to reconcile geometry and dynamics within curved spacetime, and to refine the physical consequences of general relativity at a moment when modern mathematical physics was rapidly consolidating its classical foundations. - Well preserved. - From the collection of the Atlanta gynecologist Goodman Basil Espy III (1935-2024). - Boni 236. Weil 202 ("principal work").

Baltimore, Princeton University Press, 1938 a.1940. Royal8vo. Bound in 2 full cloth, gilt lettering to spines. In: Annals of Mathematics", Series 2, Vol. 39 and vol. 40. (Entire volumes offered). The papers: pp. 65-100 a. pp. 455-464. Clean and fine.også on a generalization. pais p. 496 First appearance of these two importent papers on the General theory of Relativity, in which is shown that the equation of motion follows directly from the field equation that defined the geometry."Einstein's last importent contribution to general relativity deals again with the problem of motion. It is the work done with Leopold Indfeld and Banesh Hoffmann on the N-body problem of motion. In these papers, the gravitational field is no longer treated as external. Instead, it and the motion of its (singular) sources are treated simultaneously. A new approximation scheme is introduced in which the fields are no longer necessarily weak but in which the source velocities are small compared with the light velocity. (These equations) are widely used in analyses of planetary orbits in the solar system."(Pais "Subtle is the Lord", pp. 290-91).Weil: 202 a. 205, both with an asterix, denoting a major paper. - Boni: 236 a. 236.1.

(Princeton, NJ.), Annals of Mathematics, 1938 a. 1940. Both papers in orig. printed wrappers. Offprints from "Annals of Mathematics", Vol. 39, No. 1, january, 1938 and Vol. 41, No. 2, April, 1940. Pp. 65-100 and pp. 455-464. Both clean and fine. This copy has belonged to Abraham Pais (1918-2000) - the famous Einstein scholar, theoretical physicist and Einsteins collegue at Princeton - and having his name on top of both frontwrappers "A Pais". First editions, in the scarce offprint versions, of Einstein's last and highly important contributions to General relativity, and in which is shown that the equation of motion follows directly from the field equation that defined the geometry."Einstein's last importent contribution to general relativity deals again with the problem of motion. It is the work done with Leopold Infeld and Banash Hoffmann on the N-body problem of motion. In these papers, the gravitational field is no longer treated as external. Instead, it and the motion of its (singular) sources are treated simultaneously. Anew approximationscheme is introduced in which the fields are no longer necessarily weak but in which the source velocities are small compared with the light velocity . The equations obtained have found use in situations where Newtonian interaction must be included. '(These equations) are widely used in analyses of planetary orbits in the solarsystem. For example, the Cal Tech Jet Propulsion Laboratory uses them, in modified form, to calculate ephmerides for high-precision tracking of planets and spacecraft."(Pais "Subtle is the Lord", p. 290-91)."The problem of the equation of motion of bodies is the following. The 1916 theory had a classical structure in the sense that there were both field equations (the curvature of space-time is determined by the mass and motion of bodies in space-time) and equations of motion of bodies (the world line of small mass is a geodesic). Are these two statements really separate? If the field equations were linear, they indeed would be. They are not linear, however, and Einstein showed (in the papers offered) that if matter is represented by a point singularity of the metric field, these singularities are located on world lines that are geodesics of space-time, provided its metric satisfies the equation of general relativity."(DSB).Weil: 202 a. 295 (both with an asterix denoting a major paper). - Boni: 236 a. 236.1.