Linear perturbations of spatially locally homogeneous spacetimes

Tanimoto, Masayuki

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Linear perturbations of spatially locally homogeneous spacetimes

MPS-Authors

Tanimoto, Masayuki
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

59725.pdf
(Preprint), 249KB

Supplementary Material (public)

There is no public supplementary material available

Citation

Tanimoto, M. (2003). Linear perturbations of spatially locally homogeneous spacetimes. Contemporary Mathematics / AMS, 337, 171-185.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-532E-3

Abstract

Methods and properties regarding the linear perturbations are discussed for some spatially closed (vacuum) solutions of Einstein's equation. The main focus is on two kinds of spatially locally homogeneous solution; one is the Bianchi III (Thurston's H^2 x R) type, while the other is the Bianchi II (Thurston's Nil) type. With a brief summary of previous results on the Bianchi III perturbations, asymptotic solutions for the gauge-invariant variables for the Bianchi III are shown, with which (in)stability of the background solution is also examined. The issue of linear stability for a Bianchi II solution is still an open problem. To approach it, appropriate eigenfunctions are presented for an explicitly compactified Bianchi II manifold and based on that, some field equations on the Bianchi II background spacetime are studied. Differences between perturbation analyses for Bianchi class B (to which Bianchi III belongs) and class A (to which Bianchi II belongs) are stressed for an intention to be helpful for applications to other models.