Linear perturbations of spatially locally homogeneous spacetimes

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.Comment: Eq.(2.2) and Eq.(3.1) swapped. Errata to the (yet-to-be) published version attached. 16 pages, to appear in Contemporary Mathematics, AM

Prediction on CP Violation in Long Baseline Neutrino Oscillation Experiments

We predict CP violation in the long baseline accelerator experiments taking into consideration the recent LSND data and the atmospheric neutrino data. The estimated upper bound of CP violation is 0.006, which may be observable in the long baseline accelerator experiments. It is found that the upper bound increases to 0.01 if the LSND data is excluded. The matter effect, which is not CP invariant, is found to be very small in the case we consider.Comment: 23 pages, LaTex file, 4 figures included using epsfig fig.3 and 4 are added. To be published in PT