A solution of the Cauchy initial value problem in the nonsymmetric theory of gravitation

The Cauchy initial value problem in a theory of gravity based on a nonsymmetric Hermitian metric is investigated. The field equations are solved in terms of a series expansion of the metric gμν. In the nth order the equations take the form of either second-order hyperbolic partial differential equations for gij (i, j=1,2,3) or a first-order equation for the vector gauge field Wi. Given initial data on a space-like surface S (x0=0), the integration forward in time of the equations can be performed, assuming that the field variables are reasonably smooth and analytic.