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Abstract
摘要 |
Most general master equations are obtained for the linear gravitational perturbation theory in (m+n)-dimensional spacetimes with warped product metrics. These new master equations do not depend upon the spectral of the Laplace-type operators of some Einstein manifolds which can be viewed as n-dimensional submanifolds of the spacetimes, and provide a useful toolkit to study other gauge-invariant perturbation theories. In the case of m=2, we introduce Teukolsky-like gauge-invariant variables without using any special frame. For an Einstein spacetime, we find these gauge -invariant variables suggest a natural geometric explanation for Kodama-Ishibashi variables. Starting from Penrose wave equation for the Einstein spacetime, we find that the linear perturbation equations by these variables form a closed system. We show these equations are decoupled in some special cases by using our generalized master equations. |
