A metric for an Evans-Vigier field

In this paper we present an example of a specific metric which geometrizes explicitly a light-like four-vector potential field (Evans-Vigier field). We define the concepts of 'semilocal' and 'complete' geometrization and show that a light-like vector field has the same geometrical structure as a gravitational Kerr field. With this background in mind we discuss a theoretical proposition that a rotating body generates, besides a special gravitational field, a magnetic-type gauge field which might be identified with a geometrized Evans-Vigier field. We finally present a discussion which inform us that a classical Evans-Vigier field represents a novel type of field because we cannot identify it with any of the known electromagnetic fields.