Investigation of large-scale spacetime structures in higher-dimensional cosmology

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The major research achievements obtained by my investigations from 2003 to 2005 are summarized as follows :A)Perturbation theory of higher-dimensional static black holes : For the Einstein-Maxwell system with cosmological constant in arbitrary dimensions, we showed in terms of the gauge-invariant formulation that perturbation equations for a generalized static black holes can be reduced to decoupled 2^<nd>-order ordinary differential equations of the Schrodinger type (master equations) and we derived the explicit expressions for the effective potentials and source terms for the first time in the world. Further, with the help of this formulation, we proved that the Schwarzschild black hole of arbitrary dimensions and charged black holes in four and five dimensions with non-negative cosmological constant are perturbatively stable.B)Perturbative uniqueness of higher-dimensional black holes : We proved the perturbative uniqueness of asymptotically de Sitter regular black holes in four dime … More nsions and asymptotically flat or anti-de Sitter regular black holes in arbitrary dimensions.C)Stability of flux compactification : We have shown generally that warped supersymmetric stationary solutions obtained by flux compactification in IIB supergravity are always unstable irrespective of detailed structures of the internal space and flux, and that the instability arises additively in the size modulus.D)Four-dimensional effective theory of warped compactification : For flux compactification of IIB supergravity and heterotic M-theory, we derived four-dimensional effective theories for the size modulus of the internal space and the four-dimensional metric taking account of warping for the first time in the world. Further, we pointed out that this effective theory allows a wider class of solutions than the original higher-dimensional theories.E)Exact light-like solutions in M-theory : We obtained a general class of light-like solutions with 16 supersymmetries in eleven-dimensional supergravity. These solutions in general contain more than one arbitrary functions of a single variable and can be used to study dynamics of compactifications. Less