In this paper we present an example of a specific metric which geometr
izes explicitly a light-like four-vector potential field (Evans-Vigier
field). We define the concepts of 'semilocal' and 'complete' geometri
zation and show that a light-like vector field has the same geometrica
l structure as a gravitational Kerr field. With this background in min
d we discuss a theoretical proposition that a rotating body generates,
besides a special gravitational field, a magnetic-type gauge field wh
ich might be identified with a geometrized Evans-Vigier field. We fina
lly 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.