Geometric structures of the classical general relativistic phase space
  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. 
Josef Jany\v{s}ka, Marco Modugno