Three-dimensional space-times
type: Item
instance of: scholarly article
title: Three-dimensional space-times
zbMATH Open document ID: 0629.53022
DOI: 10.1007/BF00759150
author: B. George
published in: General Relativity and Gravitation
publication date: 1987-01-01T00:00:00Z
review text: The paper gives a detailed study of three-dimensional space-times following the null tetrad formalism of Newman-Penrose (NP) applied to the three-dimensional case. The theory is developed with a real triad made up of two normalized null vectors and a unit space-like vector with space- time metric signature \((+ + -).\) According to the definitions of the Newman-Penrose Ricci rotations coefficients, the component relations of the Ricci and Bianchi identities are calculated and the algebraic classification (Segré type) of the three-dimensional Ricci tensor is studied showing four distinct types just as in the case of four-dimensional space-times. The field equations in NP-spin components form are given for topologically massive fields following the Deser, Jackiw and Templeton space-time action with topological mass. Using the algebraic classification of the Ricci tensor into these equations, two exact solutions were obtained: one is characterized by a null geodesic eigencongruence of the Ricci tensor (one of the null vector is an eigenvector of the Ricci tensor, Segré type \(\{\) \(3\})\) and the other, a Segré type \(\{\) 111\(\}\), by the fact that all the polynomial invariants constructed from the curvature are constant. The metric forms for both solutions are exhibited explicitly.
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 83C20
zbMATH DE Number: 4024206
zbMATH Keywords: Newman-Penrose formalism
zbMATH Keywords: three-dimensional space-times
zbMATH Keywords: Segré type
zbMATH Keywords: field equations
zbMATH Keywords: exact solutions
reviewed by: Waldir L. Roque
MaRDI profile type: Publication
cites work: The classification of the Ricci tensor in general relativity theory
cites work: An Approach to Gravitational Radiation by a Method of Spin Coefficients
Wikidata QID: Q125866485
full work available at URL: https://doi.org/10.1007/bf00759150
OpenAlex ID: W2042717408
description: scientific article; zbMATH DE number 4024206