Geometrical Structure of Brane Universes

1.研究膜宇宙模型的整体结构。阐明了均匀和各向同性膜宇宙的初始大爆炸奇点是点状的，因而模型中不存在视界问题。研究表明，引力波的传播速度明显超过光速，在闵可夫斯基时空中作用于嵌入物体（如膜）产生等距群的Killing矢量场可分为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，它表明，一个黑弦视界可能出现，如果物质分布是足够薄的。提出了关于黑洞视界形成的充要条件的“超箍猜想”，明确地构造了视界为压扁三维球的黑洞.在弦理论和M理论的启发下，研究了显式Einstein度规。利用5维反de Sitter Kerr黑洞构造了紧致空间上新的Einstein度量.从AdS/CFT对应的角度阐明了度量的属性。

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.