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Investigation of the Cosmic Censorship Hypothesis in Terms of Classification of Terminal Singularities

从终端奇点的分类角度研究宇宙审查假说

基本信息

批准号：
11640273
负责人：
KODAMA Hideo
金额：
$ 1.92万
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：
1999
资助国家：
日本
起止时间：
1999 至 2002
项目状态：
已结题

项目摘要

Major results of this research project are summarized as follows.1. Perturbation of the Tolman-Bondi Solution (Nakao): In order to see the stability and physical effects of naked singularities produced by gravitational collapse of dust, we investigated the behavior of perturbations of the solution. We found that the energy flux of gravitational perturbation diverges at the Cauchy horizon, but the total emitted energy is of the order of the Planck energy within the classical regime.2. Spacetime structure of the Tomimatsu-Sato solution (Kodama): In order to investigate the structure of singularities formed by non-spherically symmetric gravitational collapse, we examined in detail the structure of the Weyl and the Tomimatsu-Sato solutions, which are the most famous stationary axisymmetric vacuum solutions to the Einstein equations containing naked singularities. We showed that these spacetimes have quite richer structure which has not been recognized so far.3. Classification of compact Bi … More anchi models (Kodama): We have succeeded in giving a complete classification of spatially compact and locally homogeneous universe models with and without perfect fluid. As a consequence, we showed that models whose space is of the Thurston-type H^2xR or SL_2R have the largest dynamical degrees of freedom.4. Perturbation of the brane-world model (Kodama): We gave a complete gauge-invariant formulation for perturbations of higher-dimensional spacetimes with a partial spatial symmetry, including the brane-world model, for the first time in the world, and provided a basis for the investigation of structure formation in higher-dimensional models. Further, using this formalism, we pointed out instabilities of some cosmological solutions of the Horava-Witten model.5. Singularities and black holes in higher-dimensional theories (Kodama, Nakao): We determined all possible configurations of a vacuum brane in static and spherically symmetric spacetimes with arbitrary dimensions, and on the basis of this, we proved that there exists no brane configuration which contains a regular black hole, in such spacetimes. Further, we pointed out some rigidity properties of the vacuum brane in higher-dimensional static spacetimes satisfying the Einstein equations. We also showed that the hoop conjecture does not hold in higher dimensions, by constructing initial value data for higher-dimensional Einstein theory numerically. Less

本课题的主要研究成果如下：1.托尔曼-邦迪解的扰动（中尾）：为了了解尘埃引力坍缩产生的裸奇点的稳定性和物理效应，我们研究了解的扰动行为。我们发现，引力微扰的能流在柯西视界处发散，但总的辐射能量在经典体系内为普朗克能量的量级. Tomimatsu-Sato解的时空结构（Kodama）：为了研究由非球对称引力坍缩形成的奇点的结构，我们详细研究了Weyl和Tomimatsu-Sato解的结构，它们是爱因斯坦方程中最著名的包含裸奇点的稳态轴对称真空解。我们证明了这些时空具有迄今为止尚未认识到的相当丰富的结构.致密Bi的分类 ...更多信息 anchi型号（Kodama）：我们已经成功地给出了一个完整的分类空间紧凑的和局部均匀的宇宙模型，有和没有理想流体。因此，我们证明了空间为Thurston型H^2xR或SL_2R的模型具有最大的动力学自由度。膜世界模型的扰动（Kodama）：我们在世界上第一次为具有部分空间对称性的高维时空（包括膜世界模型）的扰动给出了完整的规范不变公式，并为研究高维模型中的结构形成提供了基础。进一步，利用这种形式主义，我们指出了Horava-Witten模型的一些宇宙学解的不稳定性.高维理论中的奇点和黑洞（Kodama，Nakao）：我们确定了任意维静态球对称时空中真空膜的所有可能构型，并在此基础上证明了在这样的时空中不存在包含规则黑洞的膜构型。进一步指出了满足爱因斯坦方程的高维静态时空中真空膜的刚性性质。我们还表明，箍猜想不成立，在高维，通过构建高维爱因斯坦理论的数值初值数据。少