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@article{778444, author = {Janyška, Josef and Modugno, Marco}, article_number = {5}, keywords = {Spacetime; phase space; spacetime connection; phase connection; Schouten bracket; Froelicher Nijenhuis bracket; symplectic structure; Poisson structure; Jacobi structure}, language = {eng}, issn = {0219-8878}, journal = {International Journal of Geometrical Methods in Modern Physics}, title = {Geometric structures of the classical general relativistic phase space}, url = {http://www.worldscinet.com/ijgmmp/ijgmmp.shtml}, volume = {5}, year = {2008} }
TY - JOUR ID - 778444 AU - Janyška, Josef - Modugno, Marco PY - 2008 TI - Geometric structures of the classical general relativistic phase space JF - International Journal of Geometrical Methods in Modern Physics VL - 5 IS - 5 SP - 699-754 EP - 699-754 PB - World Scientific SN - 02198878 KW - Spacetime KW - phase space KW - spacetime connection KW - phase connection KW - Schouten bracket KW - Froelicher Nijenhuis bracket KW - symplectic structure KW - Poisson structure KW - Jacobi structure UR - http://www.worldscinet.com/ijgmmp/ijgmmp.shtml N2 - This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the geometric conditions by which the Lorentz metric and a connection of the phase space yield contact and Jacobi structures. In particular, we specialise these conditions to the cases when the connection of the phase space is generated by the metric and an additional tensor. Indeed, the case generated by the metric and the electromagnetic field is included, as well. ER -
JANYŠKA, Josef and Marco MODUGNO. Geometric structures of the classical general relativistic phase space. \textit{International Journal of Geometrical Methods in Modern Physics}. World Scientific, 2008, vol.~5, No~5, p.~699-754. ISSN~0219-8878.
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