Ohm's Law for Plasma in General Relativity and Cowling's Theorem

Details Ohm's Law for Plasma in General Relativity and Cowling's Theorem Ohm's Law for Plasma in General Relativity and Cowling's Theorem

2010-08-18

arxiv.org/abs/1008.3025v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

Accepted for publication in Astrophysics & Space Science

Scientific paper

The general-relativistic Ohm's law for a two-component plasma which includes the gravitomagnetic force terms even in the case of quasi-neutrality has been derived. The equations that describe the electromagnetic processes in a plasma surrounding a neutron star are obtained by using the general relativistic form of Maxwell equations in a geometry of slow rotating gravitational object. In addition to the general-relativistic effect first discussed by Khanna \& Camenzind (1996) we predict a mechanism of the generation of azimuthal current under the general relativistic effect of dragging of inertial frames on radial current in a plasma around neutron star. The azimuthal current being proportional to the angular velocity $\omega$ of the dragging of inertial frames can give valuable contribution on the evolution of the stellar magnetic field if $\omega$ exceeds $2.7\times 10^{17} (n/\sigma) \textrm{s}^{-1}$ ($n$ is the number density of the charged particles, $\sigma$ is the conductivity of plasma). Thus in general relativity a rotating neutron star, embedded in plasma, can in principle generate axial-symmetric magnetic fields even in axisymmetry. However, classical Cowling's antidynamo theorem, according to which a stationary axial-symmetric magnetic field can not be sustained against ohmic diffusion, has to be hold in the general-relativistic case for the typical plasma being responsible for the rotating neutron star.

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