Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 25, Issue 3, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/25/3/035007
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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 the 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 Godel-type spacetimes in three-dimensional general relativity. The conditions for local space and time homogeneity are derived and the equivalence of three-dimensional Godel-type spacetimes is studied and the results compared with previous work on four-dimensional Godel-type spacetimes.
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