Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-10-23
Class.Quant.Grav. 20 (2003) 1879
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravit
Scientific paper
10.1088/0264-9381/20/9/319
Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.
Moncrief Vincent
Tanimoto Masayuki
Yasuno Katsuhito
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