This article is intended to give a review of the history of the classical aspects of unified field theories in the 20th century. It includes brief technical descriptions of the theories suggested, short biographical notes concerning the scientists involved, and an extensive bibliography. The present first installment covers the time span between 1914 and 1933, i.e., when Einstein was living and working in Berlin — with occasional digressions into other periods. Thus, the main theme is the unification of the electromagnetic and gravitational fields augmented by short-lived attempts to include the matter field described by Schrödinger’s or Dirac’s equations. While my focus lies on the conceptual development of the field, by also paying attention to the interaction of various schools of mathematicians with the research done by physicists, some prosopocraphical remarks are included.

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This is a comprehensive study of spatially homogeneous and SO(3)-isotropic exact solutions of the 10-parameter Lagrangian of the 'Poincare gauge theory'. Some sets of new exact solutions are presented. In particular, all solutions following from the so-called modified double quality ansatz are obtained, up to integration of some familiar ordinary differential equations. For certain classes of solutions, the occurrence of torsion singularities is discussed in detail. Furthermore, the authors investigate whether some solutions without metric singularity can provide reasonable cosmological models.

A generalized Lane-Emden equation with indices (␣,␤,,n) is discussed, which reduces to the Lane-Emden equation proper for ␣ϭ2, ␤ϭ1, ϭ1. General properties of the set of solutions of this equation are derived, and exact solutions are given. These include a singular solution without free integration constant for arbitrary n and for particular relations between n, , and ␣. Among the two-parameter solutions nonequivalent families of solutions of the same equation are obtained.

Between 1941 and 1962, scalar-tensor theories of gravitation were suggested four times by different scientists in four different countries. The earliest originator, the Swiss mathematician W. Scherrer, was virtually unknown until now whereas the chronologically latest pair gave their names to a multitude of publications on Brans-Dicke theory. P. Jordan, one of the pioneers of quantum mechanics and quantum field theory, and Y. Thiry, known by his book on celestial mechanics, a student of the mathematician Lichnerowicz, complete the quartet. Diverse motivations for and conceptual interpretations of their theories will be discussed as well as relations among them. Also, external factors like language, citation habits, or closeness to the mainstream are considered. It will become clear why Brans-Dicke theory, although structurally a déjà-vu, superseded all the other approaches.

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The present review intends to provide an overall picture of the research concerning classical unified field theory, worldwide, in the decades between the mid-1930 and mid-1960. Main themes are the conceptual and methodical development of the field, the interaction among the scientists working in it, their opinions and interpretations. Next to the most prominent players, A. Einstein and E. Schrödinger, V. Hlavatý and the French groups around A. Lichnerowicz, M.-A. Tonnelat, and Y. Thiry are presented. It is shown that they have given contributions of comparable importance. The review also includes a few sections on the fringes of the central topic like Born-Infeld electromagnetic theory or scalar-tensor theory. Some comments on the structure and organization of research-groups are also made.

The Einstein tensors of metrics having a 3-parameter group of (global) isometries with 2-dimensional non-null orbits G 3 (2, s/t) are studied in order to obtain algebraic conditions guaranteeing an additional normal Killing vector. It is shown that Einstein spaces with G 3 (2, s/t) allow a G 4 . A critical review of some of the literature on BirkhofFs theorem and its generalizations is given.