Abstract
The maximum possible proper acceleration relative to the vacuum determines much of the differential geometric structure of the space-time tangent bundle. By working in an anholonomic basis adapted to the spacetime affine connection, one derives a useful expression for the Riemann curvature scalar of the bundle manifold. The explicit documentation of the proof is important because of the central role of the curvature scalar in the formulation of an action with resulting field equations and associated solutions to physical problems.
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Brandt, H.E. Riemann curvature scalar of spacetime tangent bundle. Found Phys Lett 5, 43–55 (1992). https://doi.org/10.1007/BF00689795
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DOI: https://doi.org/10.1007/BF00689795