Magnetohydrodynamics in stationary and axisymmetric spacetimes: a fully covariant approach

Abstract

A fully geometrical treatment of general relativistic magnetohydrodynamics (GRMHD) is developed under the hypotheses of perfect conductivity, stationarity and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in GRMHD. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.

Minor modifications (text only); published version (28 pages)

References in corpus (2)

• Relativistic stars with purely toroidal magnetic fields
• Evolution of neutron stars with toroidal magnetic fields: Axisymmetric simulation in full general relativity

Cited by in corpus (12)

• General relativistic neutron stars with twisted magnetosphere
• Initial data for binary neutron stars with adjustable eccentricity
• Equilibrium solutions of relativistic rotating stars with mixed poloidal and toroidal magnetic fields
• Von Zeipel's theorem for a magnetized circular flow around a compact object
• Magnetohydrodynamic simulations of self-consistent rotating neutron stars with mixed poloidal and toroidal magnetic fields
• Magnetic equilibria of relativistic axisymmetric stars: The impact of flow constants
• Magnetically Confined Mountains on Accreting Neutron Stars in General Relativity
• Double flows anchored in a Kerr black hole horizon. I. Meridionally self-similar MHD models with loading terms
• Relativistic MHD modeling of magnetized neutron stars, pulsar winds, and their nebulae
• Methods for relativistic self-gravitating fluids: From binary neutron stars to black hole-disks and magnetized rotating neutron stars
• Toroidal magnetic fields in self-gravitating disks around black holes
• Local, Non-Geodesic, Timelike Currents in the Force-Free Magnetosphere of a Kerr Black Hole