Ohm's law for plasma in general relativity and Cowling's theorem
Abstract
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 and Camenzind (Astron. Astrophys. 307:665, 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 ω of the dragging of inertial frames can give valuable contribution on the evolution of the stellar magnetic field if ω exceeds 2.7×1017(n/σ) s‑1 (n is the number density of the charged particles, σ 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.
- Publication:
-
Astrophysics and Space Science
- Pub Date:
- February 2011
- DOI:
- 10.1007/s10509-010-0470-3
- arXiv:
- arXiv:1008.3025
- Bibcode:
- 2011Ap&SS.331..565A
- Keywords:
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- MHD;
- Plasmas;
- General relativity;
- Magnetic field;
- Astrophysics - Solar and Stellar Astrophysics;
- General Relativity and Quantum Cosmology
- E-Print:
- Accepted for publication in Astrophysics &