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

本课题的主要研究成果总结如下：Tolman-Bondi解（Nakao）的摄动：为了观察尘埃引力坍缩产生的裸奇点的稳定性和物理效应，我们研究了解的摄动行为。我们发现引力扰动的能量通量在柯西视界处发散，但发射的总能量与经典状态下的普朗克能量相当。Tomimatsu-Sato解（Kodama）的时空结构：为了研究非球对称引力坍缩形成的奇点结构，我们详细研究了Weyl解和Tomimatsu-Sato解的结构。Weyl解和Tomimatsu-Sato解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相当丰富的结构，这是迄今为止尚未被认识到的。紧致宇宙模型的分类：我们成功地给出了具有和不具有完美流体的空间紧致和局部齐次宇宙模型的完整分类。结果表明，空间为thurston型H^2xR或SL_2R的模型具有最大的动力学自由度。膜世界模型的摄动（Kodama）：我们在世界上首次给出了包括膜世界模型在内的具有部分空间对称性的高维时空摄动的完备规范不变公式，为高维模型中结构形成的研究提供了基础。在此基础上，我们进一步指出了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）：我们确定了任意维的静态和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。进一步指出了真空膜在高维静态时空中满足爱因斯坦方程的一些刚性性质。我们还通过数值构造高维爱因斯坦理论的初值数据，证明了环猜想在高维中不成立。少

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