Einstein’s connections. III - Degenerate cases of second class

Abstract

In a recent paper, I gave the solution of Einstein’s first set of equations of unified field theory, by the method of repeated substitution, and obtained the conditions for the existence and uniqueness of the solution for the first two classes of K_λμ and for all indices of inertia of h_λμ. The object of this paper is to study the solutions in the singular cases of the second class when these conditions are not satisfied. It may, however, be noted that Hlavaty studied the singular solutions both in non-holonomic form and holonomic form. In this paper, the singular solutions will be obtained in other holonomic forms using the solution obtained by me for non-degenerate case.