Fermi-Walker gauge in 2+1 dimensional gravity.

TL;DR

This paper demonstrates that the Fermi-Walker gauge simplifies solving the metric in 2+1 dimensional gravity with sources, providing explicit formulas and classifications, and shows that energy conditions prevent closed timelike curves in symmetric cases.

Contribution

It introduces explicit solving formulas for the metric in the Fermi-Walker gauge for stationary and circularly symmetric cases, linking solutions to Wilson loop invariants and energy conditions.

Findings

Solutions classified by Wilson loop invariants.

Energy conditions imply absence of closed timelike curves.

Explicit formulas for stationary and circularly symmetric metrics.

Abstract

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