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

高维宇宙学中大尺度时空结构的研究

基本信息

批准号：
15540267
负责人：
KODAMA Hideo
金额：
$ 1.79万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

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

本文从2003年到2005年的研究工作中，主要取得了以下成果：（1）高维静态黑洞的微扰理论：对于任意维宇宙常数的Einstein-Maxwell系统，我们证明了广义静态黑洞的微扰方程可以通过规范不变形式化为解耦的2^<nd>阶Schrodinger型常微分方程（主方程），并在国际上首次导出了有效势和源项的显式表达式。进一步，我们证明了任意维的Schwarzschild黑洞以及四维和五维的具有非负宇宙学常数的带电黑洞都是微扰稳定的.B）高维黑洞的微扰唯一性：我们证明了四维渐近de Sitter正则黑洞的微扰唯一性 ...更多信息 nsions和渐近平坦或anti-de Sitter规则黑洞在任意维. C）通量紧致化的稳定性：我们已经一般地证明了在IIB超引力中通过通量紧致化得到的翘曲超对称定态解总是不稳定的，与内部空间和通量的详细结构无关，并且不稳定性在尺寸模中增加.D）四维有效翘曲紧致化理论：对于IIB超引力的通量紧致化和杂化M理论，我们在国际上首次导出了考虑翘曲的四维有效内部空间尺寸模和四维度规理论. E）M-理论中的精确类光解：我们在11维超引力中得到了具有16个超对称的一般类光解。这些解一般包含多个单变量的任意函数，可以用来研究紧化的动力学。少