Complementarity of kinematics and geometry in general relativity

S.S. Kokarev1

Abstract

Relations between the kinematics, geometry (metric) and the law of motion for reference frames are considered in the context of general relativity. More specifically, we analyze the question, to what extent each pair from the three above-mentioned objects determines the third one. It is well known that the metric and the reference frame uniquely determine all kinematic tensors (the acceleration, deformation and spin forms). We show that the kinematic tensors together with the motion of the reference frame determine the geometry up to arbitrary functions of the spatial coordinates if a single integrability condition for the angular velocity tensor is satisfied. In the case where the motion of the reference frame is specified, there emerges rather a complicated set of consistency conditions of both algebraic and differential nature. Some aspects of the geometrization principle, Poincare's geometric conventionalism and a relativistic analogue of the quantum-mechanical complementarity principle are discussed in the light of the results obtained.

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