Masayuki Tanimoto 2004 Class. Quantum Grav. 21 5355 doi:10.1088/0264-9381/21/23/005
Scalar fields on SL(2, R) and H2 × R geometric spacetimes and linear perturbations
Masayuki Tanimoto
Show affiliationsUsing appropriate harmonics, we study the future asymptotic behaviour of massless scalar fields on a class of cosmological vacuum spacetimes. The spatial manifold is assumed to be a circle bundle over a higher genus surface with a locally homogeneous metric. Such a manifold corresponds to the 
-geometry (Bianchi VIII type) or the H2 × R-geometry (Bianchi III type). After a technical preparation including an introduction of suitable harmonics for the circle-fibred Bianchi VIII to separate variables, we derive systems of ordinary differential equations for the scalar field. We present future asymptotic solutions for these equations in a special case, and find that there is a close similarity with those on the circle-fibred Bianchi III spacetime. We discuss the implications of this similarity, especially for (gravitational) linear perturbations. We also point out that this similarity can be explained by the fibre term dominated behaviour of the two models.
- PACS
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98.80.Jk Mathematical and relativistic aspects of cosmology
04.25.Nx Post-Newtonian approximation; perturbation theory; related approximations
- MSC
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83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries
- Subjects
- Dates
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Issue 23 (7 December 2004)
Received 30 June 2004, in final form 11 October 2004
Published 9 November 2004
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Scalar fields on SL(2, R) and H2 × R geometric spacetimes and linear perturbations
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