Global Structure of Spacetime and Quantum Mechanics

点击翻译按钮获取中文摘要

(1) Quantum Field Theory and Naked SingularityWe have studied a simple model of quantum field theory in 1+1 dimensions to understand the effect of time like naked singularity. Specifically we have studied the quantum radiation by a sudden change of the boundary condition from Neumann to Dirichret. We showed that the radiation travels along the null geodesic emanating from the beginning of the singularity, which can be called "thunderbolt".(2) Black Hole and Quantum Information TheoryWe applied quantum information theory to black hole physics. We showed that the increase of the generalized entropy by quantum process outside the horizon of a black hole is more than the Holevo bound of mutual information between a message prepared by an agent located outside the horizon and that received by an observer at infinity. In the optimal case, the prepared information can be completely retrieved.(3) Information Theory and CosmologyThe effective evolution of an inhomogeneous cosmological model may … More be described in terms of spatially average d variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the 'Kullback--Leibler Relative Information Entropy', expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time-evolution of 'effective information' and explore some implications. We conjecture that the information content of the Universe - measured by Relative Information Entropy of a cosmological model containing dust matter -- is increasing.(4) Topology of Black HoleRecent development of numerical study of general relativity reveals interesting aspect in the gravitational collapse. The event horizon of a black hole can be topologically a torus but it becomes a sphere eventually. Siino has classified all the possible topologies of black holes using the catastrophe theories.(5) Non-commutative Geometry and Quantum UniverseSiino has studied a path integral over factor spaces induced by identification of points which differ by irrational rotations. He has attempted to link this. space with non-commutative geometries. Less