The integral theorem of generalized virial in the relativistic uniform model

TL;DR

This paper derives a generalized virial theorem in a relativistic uniform medium model, providing exact formulas for particle velocities and energies without temperature assumptions, and explores its relation to the cosmological constant.

Contribution

It introduces a new relativistic virial theorem using generalized momenta, linking particle dynamics to cosmological parameters and clarifying energy contributions from fields.

Findings

Exact formulas for radial velocity and RMS speed of particles.

Relation established between virial theorem and cosmological constant.

Clarification of kinetic energy versus energy of motion in relativistic context.

Abstract

In the relativistic uniform model for continuous medium the integral theorem of generalized virial is derived, in which generalized momenta are used as particles momenta. This allows us to find exact formulas for the radial component of the velocity of typical particles of the system and for their root-mean-square speed, without using the notion of temperature. The relation between the theorem and the cosmological constant, characterizing the physical system under consideration, is shown. The difference is explained between the kinetic energy and the energy of motion, the value of which is equal to half the sum of the Lagrangian and the Hamiltonian. This difference is due to the fact that the proper fields of each particle have mass-energy, which makes an additional contribution into the kinetic energy. As a result, the total energy of motion of particles and fields is obtained.