Grad-Shafranov equation in noncircular stationary axisymmetric spacetimes

Details Grad-Shafranov equation in noncircular stationary axisymmetric spacetimes Grad-Shafranov equation in noncircular stationary axisymmetric spacetimes

2003-02-26

arxiv.org/abs/gr-qc/0302106v6

Phys.Rev.D67:124026,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, accepted for publication in Physical Review D, proof corrections added

Scientific paper

10.1103/PhysRevD.67.124026

A formulation is developed for general relativistic ideal magnetohydrodynamics in stationary axisymmetric spacetimes. We reduce basic equations to a single second-order partial differential equation, the so-called Grad-Shafranov (GS) equation. Our formulation is most general in the sense that it is applicable even when a stationary axisymmetric spacetime is noncircular, that is, even when it is impossible to foliate a spacetime with two orthogonal families of two-surfaces. The GS equation for noncircular spacetimes is crucial for the study of relativistic stars with a toroidal magnetic field or meridional flow, such as magnetars, since the existence of a toroidal field or meridional flow violates the circularity of a spacetime. We also derive the wind equation in noncircular spacetimes, and discuss various limits of the GS equation.

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