Cowling's theorem in non-flat space-time
Abstract
Cowling's (1934) theorem that a stationary axially symmetric magnetic field cannot be self-maintained is proven for the case of a nonflat space-time. Under the assumptions that the space-time and the electromagnetic field are stationary and axisymmetric, that fluid is moving along the trajectories of a time-like Killing vector and that the current is a pure conduction current with negligible charge density, solutions to Maxwell's equations are examined. It is shown that the only admissible solution to the equations is a magnetic field with all components equal to zero, and furthermore, that no electromagnetic fields at all exist in this case.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- March 1981
- DOI:
- 10.1093/mnras/194.4.827
- Bibcode:
- 1981MNRAS.194..827M
- Keywords:
-
- Electromagnetic Fields;
- Field Theory (Physics);
- Interstellar Magnetic Fields;
- Space-Time Functions;
- Charge Distribution;
- Maxwell Equation;
- Vectors (Mathematics);
- Astrophysics