Spherically symmetric solutions in nonsymmetrical field theories. II

Abstract

The skew symmetric tensors satisfying the general criterion of spherical symmetry, derived in Part I, contain certain arbitrary functions which indicate axial symmetry. These functions are removed. It is found that in addition to the "radial" components found by Papapetrou, the tensor has "transverse" components. In Maxwell's electrodynamics and in general relativity there are solutions which represent spherically symmetric fields of skew tensors with these transverse components. But in the unified field theories of Einstein or Schrodinger it is found that such solutions describing fields of skew tensors with nonvanishing transverse components do not exist. Thus the solutions found by Papapetrou, Wyman, and Bonnor are the only spherically symmetric solutions allowed by the unified field theories. The spherically symmetric solution found in general relativity for a radiating star has no counterpart in the unified field theories. For comparison, it is noted that the same is the case with the field equations of Dirac's new electrodynamics. Spherically symmetric nonstatic solutions of Maxwell's electrodynamics have no counterpart in Dirac's electrodynamics.