6 9 6 D O C . 4 4 3 G E N E R A L R E L A T I V I T Y A N D M O T I O N the worldtubes of the fluid particles. More general derivations in this spirit begin with Eddington 1918. For historical discussion, see Vol. 7, Doc. 63, note 6, and Havas 1989, 1993. Kennefick 2005 and Lehmkuhl 2017b provide an analysis of why Einstein had not mentioned in print the possible derivability of the equations of motion of matter along these lines since 1913. They argue that Ein- stein was unhappy with this approach because it placed constraints on the constitution of matter see also note 6. [9]See Einstein 1925w (Doc. 92), note 2, for details on Einstein’s own attempts at giving a field theoretic characterization of matter in the context of generalizations of general relativity. [10]Einstein had been convinced of the pursuit-worthiness of this approach through correspondence with George Y. Rainich see Doc. 300. [11]A reference to the Schwarzschild solution of the Einstein equations without cosmological con- stant, and to the Reissner-Nordström solution of the Einstein-Maxwell equations. For the history and interpretation of the former, see Eisenstaedt 1982, 1987, 1989 for a short history of the latter, see Einstein to Hermann Weyl, 3 January 1917 (Vol. 8, Doc. 286), note 1. [12]See Earman and Eisenstaedt 1999 for a discussion of Einstein’s thoughts on singularities during different stages of his life. [13]In the manuscript, “das Bewegungsgesetz” replaces “die Gleichgewichtsbedingungen, also wahrscheinlich das Bewegungsgesetz.” [14]Einstein had come to this realization during his correspondence with Rainich (see also note 1). By the time he wrote Doc. 300, he had become convinced that there is a fundamental difference between the linear Maxwell equations that allow for a superposition of two static one-particle solu- tions to obtain a static two-particle solution, and the nonlinear Einstein equations. Einstein had orig- inally thought that the class of static axialsymmetric solutions to the vacuum Einstein equations contained as a special case a two-particle solution that would be the analogue to the static two-particle solution of the Maxwell equations. This class of solutions was first investigated by Hermann Weyl, Tullio Levi-Civita, and Rudolf Förster (see Doc. 258, note 4, for details on the respective papers and their relations to one another. Förster used the pseudonym “Rudolf Bach” because his contract as an engineer with the company Krupp forbade him from publishing under his real name see Rudolf Förster to Einstein, 28 December 1917 [Vol. 8, Doc. 420]). [15]This metric and the canonical cylinder coordinates in which it is expressed were first given in Weyl 1917, p. 690. Einstein here uses the notation of Bach and Weyl 1922 his equations (1), (3), and (4) correspond to Bach’s equations (1), (2), and (4), respectively. ϑ is the azimuth of the meridian plane, while z and r are coordinates in this plane r = 0 is the symmetry axis of rotations. [16]Weyl 1917, p. 692, made the same point. [17]This solution is often called the Curzon-Chazy solution, which can be interpreted as the static, axialsymmetric field of a single particle the solution is thus more general than the spherically sym- metric Schwarzschild solution. Curzon 1924 and Chazy 1924 gave the field of two (now) so-called Curzon-Chazy particles. For historical discussion, see Havas 1993 and Earman 1995, pp. 17–19 for conceptual and mathematical details see Griffiths and Podolsky 2009, sec. 10.5. [18]See Weyl 1917, pp. 693–694, for Weyl’s treatment of a mass point in the canonical coordinates of a static axialsymmetric metric. [19]In modern terminology, saying that “the metric is Euclidean at infinity” corresponds to the statement that the metric is asymptotically flat. [20]The Curzon-Chazy metric has a curvature singularity at = 0, z = 0) see Scott and Szekeres 1986a, b for details of the singularity structure of the Curzon-Chazy metric, and the references given in note 17. Einstein and Grommer interpret this singularity as corresponding to a single particle, and the Curzon-Chazy metric as the field “produced” by the particle. In the language they introduce in sec. 3 below, the Curzon-Chazy metric that ψ gives rise to, via equations (6) and (1), is the “inner part” of the total metric field around the particle, whereas the metric produced by in Eq. (5a) is the “outer” part of the total metric field around the particle. Einstein and Grommer only introduce this distinction between inner and outer metric for solutions to the linearized field equations. In the case at hand, the solutions ψ to the linear Poisson equation (3) not only approximate but also generate solu- tions to the nonlinear vacuum Einstein equations, via eq. (1).. ψ
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