Equations of motion in a generalized theory of gravitation

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Abstract
The problem of the motion of test particles is studied in a theory of gravitation based on a nonsymmetric gμν. According to the conservation laws the test particles can follow two kinds of geodesies, depending on the definition of a local inertial frame in the theory. One of these geodesies is nonmaximal and leads to a timelike and null world line complete space when a new parameter l, that occurs as a constant of integration in the spherically symmetric, static solution of the field equations, satisfies . In the theory, the parameter where N is the number of fermions in a system and a is a new universal coupling constant that satisfies . The physical implications of l and the associated conservation law of fermion number is discussed in detail.

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