Abstract
The neutrino perturbations on the background of perfect fluid spacetimes with local rotational symmetry can be treated with the aid of the Debye-potential (two-component Hertz potential) formalism. This formalism reduces the Dirac equation to a single decoupled equation for a complex scalar $\ensuremath{\psi}$. The Weyl spinor pertaining to the neutrino is obtained by differentiating this scalar $\ensuremath{\psi}$. The class of spacetimes studied here contains a wide range of well-known examples. It falls naturally into three cases each of which has been investigated in detail retaining the general form of the functions appearing in the metric. It is observed that the method yields considerable information even at this general level of discussion. Finally, some specific examples, namely the G\"odel universe, the anisotropic spatially homogeneous cosmological models, and the Taub spacetime are studied illustrating the above-mentioned scheme.
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