Equivalence of three-dimensional spacetimes
Abstract
A solution to the equivalence problem in three-dimensional gravity is given and a practically useful method to obtain a coordinate invariant description of local geometry is presented. The method is a nontrivial adaptation of Karlhede invariant classification of spacetimes of general relativity. The local geometry is completely determined by the curvature tensor and a finite number of its covariant derivatives in a frame where the components of the metric are constants. The results are presented in the framework of real two-component spinors in three-dimensional spacetimes, where the algebraic classifications of the Ricci and Cotton-York spinors are given and their isotropy groups and canonical forms are determined. As an application we discuss Goedel-type spacetimes in three-dimensional General Relativity. The conditions for local space and time homogeneity are derived and the equivalence of three-dimensional Goedel-type spacetimes is studied and the results are compared with previous works on four-dimensional Goedel-type spacetimes.
Cite
@article{arxiv.0705.0758,
title = {Equivalence of three-dimensional spacetimes},
author = {F. C. Sousa and J. B. Fonseca and C. Romero},
journal= {arXiv preprint arXiv:0705.0758},
year = {2011}
}