Spherically Symmetric Solutions in Nonsymmetrical Field Theories. I. The Skew Symmetric Tensor

Abstract

The spherically symmetric form of the skew tensor $g\underset{\ifmmode \check{}\else \v{}\fi{}}{\mathrm{ik}}$, given by Papapetrou, is not sufficiently general. A more general form is found. This necessitates a reconsideration of the program of spherically symmetric solutions in nonsymmetrical field theories initiated by Papapetrou. The present paper makes a beginning in this direction.The new form of the spherically symmetric tensor $g\underset{\ifmmode \check{}\else \v{}\fi{}}{\mathrm{ik}}$ is derived from a consideration of the infinitesimal rotation of a sphere about a diameter. It is hoped to use this form to obtain nonstatic solutions in nonsymmetrical field theories which will correspond to solutions of a radiating star in general relativity.