Relativistic Kelvin circulation theorem for ideal Magnetohydrodynamics

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.