Relativistic Kelvin circulation theorem for ideal Magnetohydrodynamics

TL;DR

This paper derives a general relativistic Kelvin circulation theorem for ideal Magnetohydrodynamics and applies it to relativistic heavy ion collision models, providing a new conservation law for $T$-vorticity.

Contribution

It presents the first general expression of the relativistic Kelvin circulation theorem for ideal Magnetohydrodynamics and demonstrates its applicability to Bjorken flow in heavy ion collisions.

Findings

Derived the general relativistic Kelvin circulation theorem for ideal MHD.

Validated the theorem using analytic solutions in Bjorken flow.

Potentially applicable to relativistic heavy ion collision studies.

Abstract

We have studied the relativistic Kelvin circulation theorem for ideal Magnetohydrodynamics. The relativistic Kelvin circulation theorem is a conservation equation for the called $T$-vorticity. We have briefly reviewed the ideal magnetohydrodynamics in relativistic heavy ion collisions. The highlight of this work is that we have obtained the general expression of relativistic Kelvin circulation theorem for ideal Magnetohydrodynamics. We have also applied the analytic solutions of ideal magnetohydrodynamics in Bjorken flow to check our results. Our main results can also be implemented to relativistic magnetohydrodynamics in relativistic heavy ion collisions.