Geometrical Structure of Brane Universes

1.研究了膜宇宙模型的全局结构。阐明了均匀各向同性薄膜宇宙的初始大爆炸奇点是点状的，模型中不存在视界问题。结果表明，引力波的传播速度明显快于光速。在Minkowski时空中，作用于嵌入物体(如薄膜)上产生等距群的Kill矢量场分为7类。2.研究了高维时空中的黑色物体。在无限长物质存在的情况下，如果物质分布足够薄，则可能出现黑弦视界。提出了关于黑洞视界形成的充要条件的“超环猜想”，显式构造了视界为被挤压的三维球体形状的黑洞。在弦理论和M理论的激励下，研究了显式爱因斯坦度规。利用5维反de Sitter Kerr黑洞构造了紧致空间上的新爱因斯坦度规。从ADS/CFT对应的角度阐明了度量的性质。

1.Global structure of brane universe models is studied. It is clarified that initial big-bang singularities of homogeneous and isotropic brane universes are point-like, and then there is no horizon problem in the models. It is shown that gravitational waves can propagate apparently faster than the light speed.Killing vector fields, which generate isometry group acting on the embedded objects, e.g.branes, in the Minkowski spacetime are classified into 7 families.2.Black objects in higher dimensional spacetimes are studied. In the case of an infinitely long matter exists, it is shown that a black-string horizon could appear if the matter distribution is sufficiently thin. It is proposed that the "hyper-hoop conjecture" which is a conjecture about the necessary and sufficient condition for the formation of black hole horizon.Black holes with horizons in the shape of squashed 3-dimensional sphere are constructed explicitly. The asymptotic structure is locally flat with a compact dimension.3.Motivated by the string theory and M theory, explicit Einstein, metrics are studied. New Einstein metrics on compact spaces are constructed using 5-dimensional anti-de Sitter Kerr black hole. Properties of the metrics are clarified from the point of view of AdS/CFT correspondence.