Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008phrvd..77b4025n&link_type=abstract
Physical Review D, vol. 77, Issue 2, id. 024025
Astronomy and Astrophysics
Astrophysics
Einstein-Maxwell Spacetimes, Spacetimes With Fluids, Radiation Or Classical Fields, Relativistic Plasmas, Magnetohydrodynamics, Electric And Magnetic Fields
Scientific paper
While the definition of static equilibria is not clear in a general relativistic context, in many cases of astrophysical interest a natural 3+1 split exists which allows us to define physically meaningful spatial and temporal coordinates. We study the possibility of axisymmetric magnetohydrodynamic equilibria in this setting. The presence of a nontrivial shift velocity provides a constraint not present in the Newtonian case, while the momentum equation may be set in a Grad-Shafranov-like form with the presence of additional terms involving the space-time metric coefficients. It is found that whenever the magnetic field or the shift velocity possesses poloidal component, the existence of even local static equilibria demands that the metric parameters satisfy such strong conditions that these equilibria are extremely unlikely. Only very particular cases such as purely toroidal fields and shifts yield existence of equilibria, provided we are able to choose arbitrarily the plasma pressure and density.
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