Topics in General Relativity

Citation

Bondarescu, Mihai (2007) Topics in General Relativity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2DKM-A388. https://resolver.caltech.edu/CaltechETD:etd-05282007-231321

Abstract

This thesis is based on three of the five research projects I have worked on during my graduate student years. Each of these projects resulted in a paper a chapter of this thesis is based on. Two other papers I published during my stay at Caltech are not included, as they are not related to the research reported here.

After a brief introduction in the first chapter, in chapter two I discuss a simple way to greatly reduce tilt instability in Advanced LIGO by changing the mirror shape from nearly-flat previously considered mesa beams to nearly a nearly concentric shape that would provide the beam characteristics without the tilt instability. I also propose a family of hyperboloidal beams that join the nearly-flat and nearly-concentric mesa beams in a continuous manner.

In chapter three I report the results of a recent search for the lowest value of thermal noise that can be achieved in LIGO by changing the mirror shape. I discuss in detail the beam properties and point out some of the characteristics of an advanced LIGO that uses these beams. Such an instrument, if built, would have an event rate roughly three times higher than an advanced LIGO using the Mesa beams introduced in chapter 2.

Chapter four, which is also the last chapter of this thesis, is based on a Numerical Relativity project. I compute embeddings of general two-dimensional surfaces with spherical topology in flat 3D space using a minimization algorithm. The minimization problem is similar to the one solved in chapter three, albeit in a somewhat different setting.

Thesis Files