Geometric structures of the classical general relativistic phase space. (English) Zbl 1160.53008

The paper is devoted to the study of geometric properties of the phase space, which is interpreted as the first jet space of motions regarded as time-like one-dimensional submanifolds of space-time. In particular, the authors study the contact and Jacobi structures induced by the Lorentz metric. It is also shown that the electromagnetic field yields additional terms to the purely geometric objects of the phase space. The conditions are determined under which the geometric objects induced on the phase space by a general phase connection yield contact and Jacobi structures. A useful tool in such investigations is the geometry of jets of submanifolds and the theory of natural differential operators.


53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B15 Other connections
53D05 Symplectic manifolds (general theory)
53D17 Poisson manifolds; Poisson groupoids and algebroids
58A10 Differential forms in global analysis
58A20 Jets in global analysis
58A32 Natural bundles
Full Text: DOI arXiv


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