Cowling's theorem in nonflat spacetime
Abstract
Cowling's (1934) theorem that a stationary axially symmetric magnetic field cannot be selfmaintained is proven for the case of a nonflat spacetime. Under the assumptions that the spacetime and the electromagnetic field are stationary and axisymmetric, that fluid is moving along the trajectories of a timelike 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;
 SpaceTime Functions;
 Charge Distribution;
 Maxwell Equation;
 Vectors (Mathematics);
 Astrophysics