Fermi-Walker gauge in (2+1)-dimensional gravity

It is shown that the Fermi-Walker gauge allows a general solution for determining the metric given the sources, in terms of simple quadratures. We treat the general stationary problem providing explicit solving formulae 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 us 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 implies the total absence of closed time-like curves. The extension of this theorem to the general stationary problem in the absence of rotational symmetry is considered. At present such an extension is subject to some assumptions on the behaviour of the determinant of the dreibein in this gauge.