The general relativistic magnetohydrodynamic dynamo equation

Abstract

The magnetohydrodynamic dynamo equation is derived within general relativity, using the covariant 1 + 3 approach, for a plasma with finite electrical conductivity. This formalism allows for a clear division and interpretation of plasma and gravitational effects, and we are not restricted to a particular space–time geometry. The results should be of interest in astrophysics and cosmology, and the formulation is well suited to gauge‐invariant perturbation theory. Moreover, the dynamo equation is presented in some specific limits. In particular, we consider the interaction of gravitational waves with magnetic fields, and present results for the evolution of the linearly growing electromagnetic induction field, as well as the diffusive damping of these fields.

Magnetofluid dynamics in curved spacetime

“…Then the next step is to investigate relativistic mechanisms that, in combination with inhomogeneous thermodynamics, will create sources and sinks for H, and X. Finding the origin of seed vorticity (of the magnetic field, for instance), which could be amplified in an ideal dynamo-like mechanism, is one of the most fascinating problems of theoretical astrophysics and cosmology, and several recent papers have advanced the effort by making the special relativistic model of [1,3,4] generally covariant [5][6][7], i.e, by including gravity.…”

On the asymptotic balance between electric and magnetic energies for hydromagnetic relativistic flows

“…It is not clear what terms may be ignored in a general law: Some models are extremely complex. 9,10 The simplest course is to take an isotropic conductivity as in, e.g., Refs. 11-13, although an anisotropic one, also depending on the magnetic field size, is probably closer to reality.…”

Cosmic electromagnetic fields due to perturbations in the gravitational field

“…One can also invoke the magnetohydrodynamic MHD approximation, which is valid for cold plasmas (pressureless dust can be well approximated by a cold plasma treatment) [44] . Cold plasmas have components with non-relativistic velocities and are thus mathematically easier to deal with [22,45,46]. We consider a two component electron-ion plasma and assume that the motion properties of the plasma on macroscopic scales are captured by the center of mass 3-velocity v a of the system i.e the difference in mean velocities of the individual species is small compared with the fluid velocity.…”