Cowling's theorem in non-flat space-time

Details Cowling's theorem in non-flat space-time Cowling's theorem in non-flat space-time

Mar 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981mnras.194..827m&link_type=abstract

Monthly Notices of the Royal Astronomical Society, vol. 194, Mar. 1981, p. 827, 828.

Mathematics

Electromagnetic Fields, Field Theory (Physics), Interstellar Magnetic Fields, Space-Time Functions, Charge Distribution, Maxwell Equation, Vectors (Mathematics)

Scientific paper

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.

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