Geodesic
Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle
Archivum mathematicum, Tome 50 (2014) no. 5, pp. 297-316

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MR Zbl
The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric defines the canonical contact structure on the odd-dimensional phase space. In the paper we study infinitesimal symmetries of the gravitational contact phase structure which are not generated by spacetime infinitesimal symmetries, i.e. they are hidden symmetries. We prove that Killing multivector fields admit hidden symmetries of the gravitational contact phase structure and we give the explicit description of such hidden symmetries.
The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric defines the canonical contact structure on the odd-dimensional phase space. In the paper we study infinitesimal symmetries of the gravitational contact phase structure which are not generated by spacetime infinitesimal symmetries, i.e. they are hidden symmetries. We prove that Killing multivector fields admit hidden symmetries of the gravitational contact phase structure and we give the explicit description of such hidden symmetries.
DOI : 10.5817/AM2014-5-297
Classification : 58A20, 70G45, 70H33, 70H40, 70H45
Keywords: phase space; gravitational contact phase structure; gravitational Jacobi phase structure; infinitesimal symmetry; hidden symmetry; Killing multivector field 
Janyška, Josef. Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle. Archivum mathematicum, Tome 50 (2014) no. 5, pp. 297-316. doi: 10.5817/AM2014-5-297
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