Reduced Description of Stellar Dynamics by Moments of Gravitation Field

TL;DR

This paper introduces a new transformation for the gravitation field's potential, enabling Hamiltonian formulation and kinetic theory development for stellar dynamics, overcoming previous mathematical difficulties.

Contribution

It proposes a novel transformation of the gravitational potential based on continuity and action principles, facilitating Hamiltonian and kinetic descriptions of gravitation.

Findings

Removes mathematical issues in Jeans theory

Enables Hamiltonian formulation of gravitation

Allows kinetic theory development for stellar systems

Abstract

Because of absence of time derivatives from scalar potential as a generalized coordinate of gravitation field (GF) in action of nonrelativistic gravitating system, application of the Hamilton method for description of GF mechanics was impossible. In the paper a transformation of the generalized coordinate of GF, that is based on continuity equation and minimal action principle, is proposed. A potential vector is introduced that is similar to fixing of Hamilton gauge of the electromagnetic field. This transformation gives possibility of the calculation a Hamilton function, removes mathematical troubles of the Jeans theory (Jeans swindle) and allows to construct kinetic theory of GF using statistical mechanics methods.