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

2003 - 2005年我的主要研究成果总结如下：A)高维静态黑洞摄动理论：对于具有任意维宇宙学常数的爱因斯坦-麦克斯韦系统，我们用规范不变公式证明了广义静态黑洞的微扰方程可以化约为解耦的2^<和>阶薛定谔型常微分方程（主方程），并在世界上首次导出了有效势项和源项的显式表达式。在此基础上，进一步证明了任意维史瓦西黑洞和四维、五维非负宇宙学常数带电黑洞是微扰稳定的。B)高维黑洞的微扰唯一性：我们证明了在任意维度上的四角多密度和渐近平坦或反德西特正则黑洞的微扰唯一性。我们一般证明了IIB超重力中由通量紧化得到的翘曲超对称定解总是不稳定的，而与内部空间和通量的详细结构无关，并且不稳定性是在尺寸模量中加性产生的。D)翘曲紧化的四维有效理论：对于IIB超重力的通量紧化和异质性m理论，我们在国际上首次导出了考虑翘曲的内部空间尺寸模量和四维度规的四维有效理论。此外，我们指出这种有效的理论比原来的高维理论允许更广泛的解类。E) m理论中的精确类光解：我们得到了11维超引力中具有16个超对称的类光解的一般类光解。这些解通常包含多个单一变量的任意函数，可用于研究紧化动力学。少

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