On the Lie subalgebra of Killing-Milne and Killing-Cartan vector fields in Newtonian space-time

Abstract

The Galilean (and more generally Milne) invariance of Newtonian theory allows for Killing vector fields of a general kind, whereby the Lie derivative of a field is not required to vanish but only to be cancellable by some infinitesimal Galilean (respectively Milne) gauge transformation. In this paper, it is shown that both the Killing-Milne vector fields, which preserve the background Newtonian space-time structure, and the Killing-Cartan vector fields, which in addition preserve the gravitational field, form a Lie subalgebra.

arXiv comment8 pages

References in corpus (6)

• Galilean Isometries
• Covariant analysis of Newtonian multi-fluid models for neutron stars: I Milne-Cartan structure and variational formulation
• Covariant analysis of Newtonian multi-fluid models for neutron stars: II Stress - energy tensors and virial theorems
• Covariant analysis of Newtonian multi-fluid models for neutron stars: III Transvective, viscous, and superfluid drag dissipation
• Covariant Newtonian and Relativistic dynamics of (magneto)-elastic solid model for neutron star crust
• Newtonian mechanics of neutron superfluid in elastic star crust

Cited by in corpus (4)

• Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
• Entrainment in Superfluid Neutron Star Crusts: Hydrodynamic Description and Microscopic Origin
• Generalization of the Kutta-Joukowski theorem for the hydrodynamic forces acting on a quantized vortex
• Vortex pinning in the superfluid core of relativistic neutron stars