Abstract
A covariant canonical formulation of the motion of a rigid test body in a curved space-time is obtained from a suitable Cartan form ϑ on the tangent bundleT∘ of the bundle of Lorentz frames ∘ over the space-time manifoldV. The form ϑ (essentially equivalent to a Lagrangean) is chosen in close analogy to the corresponding 1-form in the classical Newtonian model of a rigid body and is very simple in terms of the natural geometrical structure of ∘. The presymplectic manifold (T∘,dϑ) then serves as evolution manifold of the system. One obtain the equations of motion and also a uniquely defined Poisson bracket on the set of observables defined as real valued functions on the manifold of motions. The rigid body interacts with the space-time curvature only via its spin in the same way as a spinning particle. Quadrupole and higher multiple interactions with the space-time curvature are not considered in this model.
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Supported in part by the National Research Council of Canada.
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Künzle, H.P. Dynamics of a rigid test body in curved space-time. Commun.Math. Phys. 27, 23–36 (1972). https://doi.org/10.1007/BF01649656
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DOI: https://doi.org/10.1007/BF01649656