  It is shown that the Fermi-Walker gauge allows the general solution of
determining the metric given the sources, in terms of simple quadratures. We
treat the general stationary problem providing explicit solving formulas for
the metric and explicit support conditions for the energy momentum tensor. The
same type of solution is obtained for the time dependent problem with circular
symmetry. In both cases the solutions are classified in terms of the invariants
of the Wilson loops outside the sources. The Fermi-Walker gauge, due to its
physical nature, allows to exploit the weak energy condition and in this
connection it is proved that, both for open and closed universes with
rotational invariance, the energy condition imply the total absence of closed
time like curves. The extension of this theorem to the general stationary
problem, in absence of rotational symmetry is considered. At present such
extension is subject to some assumptions on the behavior of the determinant of
the dreibein in this gauge. PACS number: 0420
