Problems in Gravitation

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This project continues a computational study of very strong field gravitational wave sources, concentrating on the interaction of black holes. Interacting black holes are described by Einstein's theory of General Relativity. Most approaches to solving the ten equations of General Relativity on the computer consider use only six of these, called the evolution equations. The remaining four, called the constraint equations, remain solved mathematically but can become problematical due to unavoidable numerical error in a computer simulation. Various computational algorithms developed under prior awards, additional ones to be developed in this project, and mathematical studies of relevant properties of the equations will be applied to a 3D constrained (i.e. using all ten equations) simulation of interacting black holes.Because the first generation of gravitational wave detectors is coming to maturity, prediction of waveforms from astrophysical gravitational wave sources, such as interacting black holes, is imperative. Recent developments, some of them originated in prior work at Texas, are coming together to allow more robust and physically relevant source simulations. These developments, very importantly, the introduction to fully constrained evolution of the Einstein equations. This has been made possible by a series of developments in this field, This work will be done with a combination of high school, undergraduate, and graduate students, and postdoctoral researchers. It will contribute to the community appreciation of science and astrophysics in particular, and will contribute to the success the LIGO and LISA gravitational wave detectors.