Stationary Axially Symmetric Fields and the Kerr Metric

In this note the axially symmetric metric for stationary gravitational field, in a slightly general form, is discussed. The vacuum field equations for this metric are given. Specialization of this metric leads to a different form of field equations previously discussed in literature. In particular, the Kerr metric is given in a new form. A justification for interpreting the Kerr metric as an exterior solution corresponding to a spinning rod or a rotating spherical body is given.