Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle. (English) Zbl 1340.70017

Janyška, Josef

Arch. Math., Brno 50, No. 5, 297-316 (2014).

The phase space of general relativistic test particle is the 1-jet space of motions. A Lorentzian metric determines a canonical contact structure on the odd-dimensional phase space. In the paper under review, the author studies infinitesimal symmetries that are the so-called hidden symmetries. He proves that Killing multivector fields admit hidden symmetries of the gravitation contact phase structure and he gives the explicit description of such hidden symmetries.

Reviewer: Martin Čadek (Brno)

MSC:

70H40	Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
70H45	Constrained dynamics, Dirac’s theory of constraints
70H33	Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
70G45	Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
58A20	Jets in global analysis
83C10	Equations of motion in general relativity and gravitational theory

Keywords:

phase space; gravitational contact phase structure; gravitational Jacobi phase structure; infinitesimal symmetry; hidden symmetry; Killing multivector field