http://arxiv.org/abs/1806.10119
In this paper we derive the post-Newtonian equations of the ideal Magnetohydrodynamics. To do so we use the modern approach to the post-Newtonian theory, where the harmonic gauge is used instead of the standard post-Newtonian gauge, and find the post-Newtonian metric in the presence of the electromagnetic fields. We show that although the electric field does not contribute in the metric (and equivalently in the curvature) of the spacetime, the magnetic field appears in the time-time component of the metric. Appearance of the magnetic field in the time-time component of the metric, in principle, leads to new relativistic contributions to the magnetohydrodynamic governing equations. Therefore, using the post-Newtonian metric, we find the relativistic corrections to the magnetohydrodynamic equations up to the first post-Newtonian order. In addition, as a usage of this derivation, we obtain a complete set of equations by which the behavior of the self-gravitating plasma can be determined in the post-Newtonian gravity.
E. Nazari and M. Roshan
Wed, 27 Jun 18
35/54
Comments: 24 pages, Comments and criticisms encouraged!