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

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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