Topics in General Relativity

摘要: This thesis is based on three of the five research projects I have worked during my graduate student years. Each these resulted in a paper chapter this on. Two other papers published stay at Caltech are not included, as they related to reported here. After brief introduction first chapter, two discuss simple way greatly reduce tilt instability Advanced LIGO by changing mirror shape from nearly-flat previously considered mesa beams nearly concentric that would provide beam characteristics without instability. also propose family hyperboloidal join and nearly-concentric continuous manner. In report results recent search for lowest value thermal noise can be achieved shape. detail properties point out some an advanced uses beams. Such instrument, if built, event rate roughly times higher than using Mesa introduced 2. Chapter four, which last thesis, Numerical Relativity project. compute embeddings general two-dimensional surfaces with spherical topology flat 3D space minimization algorithm. The problem similar one solved three, albeit somewhat different setting.