In order to perform an evolutionary calculation in General Relativity, accurate initial data is needed. A pseudospectral numerical method to solve both linear and nonlinear ordinary differential equations is introduced. We then calculate solutions to the Hamiltonian and momentum constraints for a binary black hole system utilizing such a pseudospectral method. The error resulting from the implementation is discussed at three locations in space: near the black holes, far from the black holes, and in between. A method to mimic mesh refinement through appropriate coordinate transforms is introduced with the result of lowering the maximum error in the system.
Library of Congress Subject Headings
Black holes (Astronomy)--Mathematical models; Double stars--Mathematical models; Differential equations--Numerical solutions; Spectral theory (Mathematics); General relativity (Physics)
Department, Program, or Center
School of Mathematical Sciences (COS)
James, Bradley, "Mimicking mesh refinement to construct initial data for a binary black hole system" (2013). Thesis. Rochester Institute of Technology. Accessed from
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