Spherically symmetric rigorous solutions in Bonnor’s unified field theory

Abstract

It is well known that the field equations in Einstein’s unified field theory of 1953 do not lead to the Lorentz equations of motion for electromagnetic charges. Bonnor remedied this defect by proposing a modified set of the field equations. In this paper an attempt is made to solve Bonnor’s field equations in the spherically symmetric case. The general solution of these equations in the magnetostatic case is obtained. It is found that when Bonnor’s constantp is taken to be real, the solution becomes singular of two finite nonzero values ofr analogous to the Reissner-Nordstrom solution in general relativity. On the other hand, whenp is imaginary, the solution has a finite nontrivial singularity of Schwarzschild’s type. The field equations have been solved in the magnetic case also, though the solution in this case reduces to the corresponding static solution under the usual boundary conditions. Further, it is shown that Bonnor’s theory does not favour the existence of a nonstatic spherically symmetric isolated system containing electric charge and current.