Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle

TL;DR

This paper investigates hidden symmetries in the gravitational contact structure of the phase space of a relativistic test particle, revealing that Killing multivector fields generate such symmetries and providing explicit descriptions.

Contribution

It introduces the concept of hidden symmetries in the gravitational contact phase space and characterizes them via Killing multivector fields, expanding understanding of phase space symmetries.

Findings

Killing multivector fields admit hidden symmetries

Explicit descriptions of these hidden symmetries are provided

Hidden symmetries are not generated by spacetime infinitesimal symmetries

Abstract

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.