Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach
Abstract
A fully geometrical treatment of general relativistic magnetohydrodynamics 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 general relativistic magnetohydrodynamics. 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.
- Publication:
-
Physical Review D
- Pub Date:
- May 2011
- DOI:
- 10.1103/PhysRevD.83.104007
- arXiv:
- arXiv:1101.3497
- Bibcode:
- 2011PhRvD..83j4007G
- Keywords:
-
- 04.20.-q;
- 04.40.Dg;
- 04.40.Nr;
- 52.30.Cv;
- Classical general relativity;
- Relativistic stars: structure stability and oscillations;
- Einstein-Maxwell spacetimes spacetimes with fluids radiation or classical fields;
- Magnetohydrodynamics;
- General Relativity and Quantum Cosmology;
- Astrophysics - High Energy Astrophysical Phenomena
- E-Print:
- Minor modifications (text only)