Extended Kelvin theorem in relativistic magnetohydrodynamics

TL;DR

This paper generalizes Kelvin's circulation theorem to relativistic magnetohydrodynamics, providing a new Lagrangian formulation and demonstrating conserved circulation in symmetric flows within general relativity.

Contribution

It introduces a novel version of the Lagrangian for relativistic MHD and proves a generalized Kelvin theorem applicable in curved spacetime.

Findings

Established a generalized Kelvin circulation theorem in relativistic MHD.

Derived a new Lagrangian formulation for perfect magnetohydrodynamics.

Illustrated conserved circulation in symmetric relativistic MHD flows.

Abstract

We prove the existence of a generalization of Kelvin's circulation theorem in general relativity which is applicable to perfect isentropic magnetohydrodynamic flow. The argument is based on a new version of the Lagrangian for perfect magnetohydrodynamics. We illustrate the new conserved circulation with the example of a relativistic magnetohydrodynamic flow possessing three symmetries.