Special Relativistic Magnetohydrodynamics with Gravitation

Abstract

We present a fully nonlinear and exact perturbation formulation of Einstein's gravity with a general fluid and the ideal magnetohydrodynamics (MHD) without imposing the slicing (temporal gauge) condition. Using this formulation, we derive equations of special relativistic (SR) MHD in the presence of weak gravitation. The equations are consistently derived in the limit of weak gravity and actionat-a-distance in the maximal slicing. We show that in this approximation the relativistic nature of gravity does not affect the SR MHD dynamics, but SR effects manifest themselves in the metric, and thus gravitational lensing. Neglecting these SR effects may lead to an overestimation of lensing masses.

Axion electrodynamics and magnetohydrodynamics

“…( 19) for the Schrödinger equation and Eqs. ( 23) and (24) for the axion-fluid equations are valid without the E • B terms. Still, we have trouble employing the transformations in the axion-induced charge and current densities in Eq.…”

“…The consistent weak gravity limit combined with the relativistic matter parts is available in the uniform-expansion gauge, setting the trace of extrinsic curvature uniform in space [23,24]. The g φγ -coupling term does not directly appear in gravity because it does not contribute to the energy-momentum tensor.…”

“…Notice that only Φ couples with the fields and the fluid; this is because we consider the non-relativistic order in fluid. For weak gravity limit combined with fully relativistic matter, see [23,24].…”