Abstract
This article is about a different representation of the geometry of the gravitational field, one in which the paths of test bodies play a crucial role. The primary concept is the geometry of the motion of a test body, and the relation between different such possible motions. Space-time as a Lorentzian manifold is regarded as a secondary construct, and it is shown how to construct it from the primary data. Some technical problems remain. Yang-Mills fields are defined by their holonomy in an analogous construction. I detail the development of this idea in the literature, and give a new version of the construction of a bundle and connection from holonomy data. The field equations of general relativity are discussed briefly in this context.
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Barrett, J.W. Holonomy and path structures in general relativity and Yang-Mills theory. Int J Theor Phys 30, 1171–1215 (1991). https://doi.org/10.1007/BF00671007
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DOI: https://doi.org/10.1007/BF00671007