The space-time models with dust matter that admit separation of variables in Hamilton-Jacobi equations of a test particle

TL;DR

This paper investigates space-time models with dust matter that allow separation of variables in the Hamilton-Jacobi equation for test particles, providing explicit forms of velocity and energy density.

Contribution

It characterizes dust-filled space-time models admitting privileged coordinates enabling complete separation of the Hamilton-Jacobi equation.

Findings

Explicit forms of 4-velocity fields and energy densities derived.

Identification of conditions for privileged coordinate systems.

Application to various space-time geometries.

Abstract

The characteristics of dust matter in space-time models, admitting the existence of privilege coordinate systems are given, where the single-particle Hamilton-Jacobi equation can be integrated by the method of complete separation of variables. The resulting functional form of the 4-velocity field and energy density of matter for all types of spaces under consideration is presented.