  The paper considers the problem of finding the metric of space time around a
rotating, weakly gravitating body. Both external and internal metric tensors
are consistently found, together with an appropriate source tensor. All tensors
are calculated at the lowest meaningful approximation in a power series. The
two physical parameters entering the equations (the mass and the angular
momentum per unit mass) are assumed to be such that the mass effects are
negligible with respect to the rotation effects. A non zero Riemann tensor is
obtained. The order of magnitude of the effects at the laboratory scale is such
as to allow for experimental verification of the theory.
