Properties of the Spatial Sections of the Space-Time of a Rotating System

TL;DR

This paper investigates the symmetry properties and geometric structures of spatial sections in a rotating space-time, revealing a complex Lie group symmetry and analyzing the related Hamiltonian system.

Contribution

It identifies the symmetry group of geodesic equations in rotating space-time and explores the geometric and Hamiltonian structures of the spatial sections.

Findings

The symmetry group is seven-dimensional and neither solvable nor nilpotent.

The variational symmetries form a five-dimensional solvable subgroup.

The study links the symmetries to the geometric properties of spatial sections.

Abstract

We study the symmetry group of the geodesic equations of the spatial solutions of the space-time generated by a noninertial rotating system of reference. It is a seven dimensional Lie group, which is neither solvable nor nilpotent. The variational symmetries form a five dimensional solvable subgroup. Using the symplectic structure on the cotangent bundle we study the resulting Hamiltonian system, which is closely related to the geodesic flow on the spatial sections. We have also studied some intrinsic and extrinsic geometrical properties of the spatial sections.