Fermi-Walker coordinates in 2+1 dimensional gravity

TL;DR

This paper demonstrates that Fermi-Walker coordinates simplify solving 2+1 dimensional gravity problems, showing that energy conditions prevent closed timelike curves in symmetric cases and exploring extensions beyond symmetry.

Contribution

It introduces a method using Fermi-Walker coordinates to solve 2+1 gravity problems and proves the absence of CTCs under energy conditions for symmetric cases, extending to more general scenarios.

Findings

Fermi-Walker gauge simplifies metric determination in 2+1 gravity.

Energy conditions imply no closed timelike curves in symmetric solutions.

Extension of CTC absence theorem to non-symmetric stationary solutions is discussed.

Abstract

It is shown that in 2+1 dimensions the Fermi-Walker gauge allows the general solution of the problem of determining the metric from the sources in terms of simple quadratures. This technique is used to solve the problem of the occurrence of closed time like curves (CTC's) in stationary solutions. In fact 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 axial symmetry, 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 axial symmetry is considered and at present the proof of such generalization is subject to some assumptions on the behavior of the determinant of the dreibeins in this gauge.