Homogeneous, anisotropic three-manifolds of topologically massive gravity

Journal Article · Sun Oct 01 00:00:00 EDT 1989 · Annals of Physics (New York); (USA)

DOI:https://doi.org/10.1016/0003-4916(89)90094-8· OSTI ID:5116845

Nutku, Y; Baekler, P ^[1]

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1. Istanbul Technical University, Physics Department, 80626 Maslak, Istanbul, Turkey, and Tubitak Research Institute for Basic Sciences, 41470 Gebze-Kocaeli, Turkey (TR)

We present a new class of exact solutions of Deser, Jackiw, and Templeton's theory (DJT) of topologically massive gravity which consists of homogeneous, anisotropic manifolds. In these solutions the coframe is given by the left-invariant 1-forms of 3-dimensional Lie algebras up to constant scale factors. These factors are fixed in terms of the DJT coupling constant {mu}m which is the constant of proportionality between the Einstein and Cotton tensors in 3-dimensions. Differences between the scale factors result in anisotropy which is a common feature of topologically massive 3-manifolds. We have found that only Bianchi Types VI, VIII, and IX lead to nontrivial solutions. Among these, a Bianchi Type IX, squashed 3-sphere solution of the Euclideanized DJT theory has finite action, Bianchi Type VIII, IX solutions can variously be embedded in the de Sitter/anti-de Sitter space. That is, some DJT 3-manifolds that we shall present here can be regarded as the basic constitent of anti-de Sitter space which is the ground state solution in higher dimensional generalizations of Einstein's general relativity. {copyright} 1989 Academic Press, Inc.

• OSTI ID: 5116845
• Journal Information: Annals of Physics (New York); (USA), Vol. 195:1; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GRAVITATION
TOPOLOGY
MASS
ANALYTICAL SOLUTION
ANISOTROPY
FIELD EQUATIONS
GENERAL RELATIVITY THEORY
LIE GROUPS
SPACE-TIME
THREE-DIMENSIONAL CALCULATIONS
EQUATIONS
FIELD THEORIES
MATHEMATICS
SYMMETRY GROUPS
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation