| Summary: | 博士 === 國立成功大學 === 物理學系碩博士班 === 98 === In this thesis we report on our code for numerical relativity, in which it is based on the Baumgarte-Shapiro-Shibata-Nakamura(BSSN) formulation, and the moving puncture method is applied, and an adaptive/fixed mesh refinement(AMR) is implemented. The simulation results including a single and a binary black hole system demonstrate that this code is reliable and ready to be used in the study of more realistic astrophysical scenarios and of numerical relativity.
In our universe, binary black hole systems are always located in the potential of some super-massive black hole hosted in the center of galaxy. To our knowledge, all binary black hole systems have been treated in previous studies as isolated systems by ignoring the effects of the environment in which they are located. We are interesting in the effects, and propose a perturbational scheme for investigating the effects of these background potentials on the evolution of a binary black holes, especially the gravitational radiation which is of interest for gravitational wave detection. The binary black hole systems we considered include head-on colliding and inspiralling binaries. With respect to the super-massive black hole, the free-falling and circular orbiting case are considered as two limit cases of realistic systems.
High-spinning black holes could exist at the center of some galaxies; then there are difficulties in numerically simulating it. We propose a new radial coordinate to re-write the Kerr metric in a punctured form. Unlike some coordinates introduced previously, the horizon radius can be finite, even being a constant which is independent of the size of the spin, in our new coordinate with the extreme Kerr limit a/M→1. There are three parameters in our coordinate controlling the distortion of the coordinate. Through a suitable choice, we can construct good initial data with the extreme Kerr limit. However, we need to fine tune our code to accurately simulate the extremal Kerr black hole.
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