Equivalence of three-dimensional spacetimes

Details Equivalence of three-dimensional spacetimes Equivalence of three-dimensional spacetimes

2007-05-05

arxiv.org/abs/0705.0758v2

Class.Quant.Grav.25:035007,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages - content changes and corrected typos

Scientific paper

10.1088/0264-9381/25/3/035007

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.

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