Collaborative Research: Developing Spectral Methods for Simulating Binary Black Hole Spacetimes

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This research will continue the development of the Spectral Einstein Code by the Caltech-Cornell numerical relativity collaboration. Spectral methods are ideal for problems with smooth solutions, like the vacuum Einstein equations. The exponential convergence of spectral methods will provide the needed accuracy for LIGO and LISA data analysis using currently available computer hardware. A series of crucial improvements and enhancements to this code will be made: This work is expected to allow the code to model the merger phase of binary black hole simulations; more efficient domain decompositions will be implemented; enhancements will be made that allow thecode to simulate binary black hole systems with unequal masses and unequal spins; the ability to solve second-order hyperbolic evolution systems will be added to the code; an event horizon finder will be included; implicit time stepping will be added to allow the code to follow the adiabaticinspiral phase of binary black hole evolutions more efficiently; the outer boundary conditions used by the code will be improved; more astrophysically relevant initial data will be constructed; new methods will be developed to characterize and quantitatively compare the results of numerical simulations produced by different groups using different numerical codes.This research will have a significant impact on the broader area of computational science. The computational techniques developed could be used to solve problems in many other areas, including fluid dynamics, meteorology, seismology, and astrophysics. Young researchers trained inthese techniques are in great demand. The funds from this grant will support the training of graduate students and postdoctoral scholars. This research will also have a broad impact on the understanding of fundamental physics:There are currently no real tests of general relativity in the strong field regime of black holes. For experiments like LIGO to confront theory with observation, one must be able to calculate what the theory predicts to answer questions such as: Are the black holes that LIGO may observe reallythe black holes predicted by Einstein's theory?