ANALYZING AND IMPROVING INITIAL DATA FOR BINARY BLACK HOLES - Grigsby, Jason (Wake Forest University, 2009)
Binary black holes are one of the most likely sources of gravitational radiation to be detected by projects such as LIGO and LISA. This radiation causes the binary to lose energy and angular momentum with the black holes adiabatically spiraling together. The strongest radiation is emitted at merger, where the strong fields and lack of symmetry require the use of fully numerical methods for solving Einstein's equations. Numerical simulations of binary black holes require the specification of initial data to be used with evolution equations. The physics of a binary black hole system in numerical relativity will largely be determined by the initial data. This dissertation is concerned with the analysis and improvement of that initial data. There will be two main parts to this dissertation. The first part will be concerned with how initial data is created. This starts with a presentation of the 3+1 decomposition which rewrites Einstein's field equations as a set of constraint and evolution equations. This will be followed with a discussion of the conformal thin-sandwich decomposition and excision methods which rewrite a portion of the 3+1 decomposition as a well-posed set of elliptic equations and boundary conditions that can be used to determine initial data. Then I will discuss the the physics of binary black holes, what physical measurements we can apply and how they are used to find astrophysically likely initial data for binary black holes. Lastly, there will be a discussion of the implementation of these methods. The second section will cover my own research into binary black hole initial data. I will describe tests of methods for finding binaries in quasicircular orbit, thought to be the most likely scenario for binary sources of gravitational waves. This is entwined with tests to better understand spin in binary black holes. I will then report on efforts to understand eccentricity in binary black hole initial data. Finally I will discuss efforts to improve methods for creating initial data by removing an assumption known to lead to errors --- that of conformal flatness. This is replaced by an effort to numerically determine the conformal metric.
Keywords: Theory of relativity, gravitation