Mathematics – Mathematical Physics
Scientific paper
Sep 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979jmp....20.1911c&link_type=abstract
Journal of Mathematical Physics, Volume 20, Issue 9, pp. 1911-1924 (1979).
Mathematics
Mathematical Physics
2
Fundamental Problems And General Formalism
Scientific paper
In this paper we discuss the solutions of the c-number quantum-mechanical equations of neutrino, Maxwell, and scalar fields in the background metric of a static, cylindrically symmetric magnetic or plasm universe. The magnetic universe consists of a parallel magnetic field distribution held together by the gravitational field of its own energy and stress. It is an exact solution of the Einstein-Maxwell equations for the gravitational field associated with a stationary source-free cylindrically symmetric magnetic field. The solution does not depend specifically upon the assumption that the seat of the energy-stress distribution is an electromagnetic field. A ''plasm of index 2'' would have the same metric. The main instrument of the present perturbation theory, valid in all algebraically special spacetimes, is the Cohen-Kegeles (CK) scalar wave equation for test fields of helicity h (or s). This equation, written in the updated Geroch-Held-Penrose (GHP) formalism, is made explicit for the chosen null tetrad by determining the spin coefficients and the operators of that formalism. Exact solutions of the CK wave equation are obtained for the case of zero orbital angular momentum. For the case of nonzero orbital angular momentum the JWKB approximation is used to obtain the quadratures for the orbits in the magnetic universe. It is shown that the neutrino orbits precess about the magnetic (or plasm) universe axis in a manner different from orbits of particles with helicity zero and helicity one. The expression for the neutrino precessional frequency (due to nonvanishing helicity) is given explicitly. The photon precessional frequency is twice that for neutrinos. Finally, the CK procedure is compared with that of Teukolsky for finding the neutrino and Maxwell fields in type D spacetimes.
Cattell David F.
Melvin M. A.
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