The potentials of the acceleration field and pressure field in rotating relativistic uniform system

TL;DR

This paper calculates the scalar and vector potentials of acceleration and pressure fields in a rotating relativistic uniform system, revealing how rotation influences these potentials and their dependence on angular velocity.

Contribution

It introduces a novel method for calculating potentials in rotating systems considering multiple bodies and compares relativistic potentials with non-rotating cases.

Findings

Rotation induces vector potentials aligned with linear velocity.

Proper random motion has a minor effect on the fields compared to rotation.

Derived a relativistic pressure formula linking pressure, density, and particle velocity.

Abstract

The scalar and vector potentials of the acceleration field and the pressure field are calculated for the first time for a rotating relativistic uniform system, and the dependence of the potentials on the angular velocity is found. These potentials are compared with the potentials for the non-rotating uniform system that have been found previously. The rotation leads to the appearance of vector potentials, which at each point turn out to be directed along the corresponding linear velocity of rotation. The calculation shows that for rotating stellar objects the contribution to the fields vector potentials from the proper random motion of particles is small compared to the contribution from rotation and may not be taken into account. From the expression for the pressure field potential a relativistic formula follows that relates the pressure, mass density, and mean square velocity of the particles. This formula in the limit of low speeds corresponds to the expression for the pressure in molecular kinetic theory. When calculating the potentials, a new method is used that takes into account the potentials of two different bodies, a cylinder and a sphere, for solving the wave equation of rotating system.