This award supports a program of research aimed at the development of new computer software that will allow researchers simulating the evolution and merger of astronomical systems containing two black holes to identify and characterize the gravitational waves produced in the simulations. Gravitational waves produced in the last moments of binary black hole evolutions are expected to be an important signal for the Laser Interferometer Gravitational-wave Observatory (LIGO). Searches of LIGO data for signals of this type can be made more sensitive if more is known about the waveforms to be expected. The proposed software will use the technique of Cauchy-characteristic wave extraction, a method that can analyze the waveforms infinitely far from the source (in effect where LIGO would be). Standard methods could introduce inaccuracies into the extracted waveforms because they require measurement much closer to the source. The developed software will be made available to the broader research community as a module of the Cactus framework. Undergraduates will be supported by this award. The science and methods of this project will form the basis of public lectures by the PI.
Gravitational wave astronomy will uncover facets of our universe that are otherwise invisible to conventional astronomy – which relies on light. The goal of my research is to compute gravitational wave patterns, and to prepare templates for observatories to identify the signal. My work consists in solving Einstein’s equations of general relativity numerically, using computer approximations, for space-times that are too complicated to solve exactly. The numerical approach used in this project, called the "Cauchy-characteristic extraction" method, is the most precise method for the computation of gravitational waveforms at infinity from binary black holes. The characteristic method offers a clean description of the radiated waveform in terms of compactified light cones, which computes the gravitational waves infinitely far from their source. However, this method has its limitations: it cannot get too close to the source, because of the complicated caustics that are inherent in strong gravitational fields. The solution to this problem is to match the characteristic code with a Cauchy black hole simulation code, obtaining a "Cauchy-characteristic" code. In order to do this, we need to solve the problem of matching the inner computational boundary of the characteristic code with the outer computational boundary of a Cauchy code. As part of this research project, we developed, calibrated, and made publicly available a characteristic waveform extraction tool, the PITT code, which is now part of the Einstein Toolkit, a collection of open software for relativistic astrophysics. We proved that the numerical code produces waveforms whose numerical truncation error satisfies the demands of next generation detectors, without any recourse to linearization, and from small extraction radii. These results surpass existing numerical simulations, which are sufficiently accurate to make gravitational wave templates for current searches of ground-based detectors. Another component of my research interest is the problem of the boundaries, which is not yet fully solved for any of the present black hole codes. The physical picture underlying the null-timelike problem for Einstein’s equations is that it has two initial boundaries: the outgoing gravitational radiation emanating from interior matter sources, and the ingoing radiation incident on the system represented by the initial null data. The accuracy of the waveform extracted by the characteristic code depends critically on those boundaries. At present, it is known how to treat boundaries in the harmonic formulation of Einstein’s equations and a tetrad formulation of the Einstein-Bianchi system. However, in the characteristic formulations, there is not yet a well-defined way of treating the boundaries. One purpose of this research initiative was to explore the solutions to specific boundary problems arising from the matching of computational domains. My research won’t be complete without involving undergraduate and graduate student in research. One major component of student involvement consists in monitoring the simulation runs and developing visual displays of the data generated by the simulations. This part of the research is separable from the more abstract problem of implementing the algorithms. Visualization is a very important part of numerical simulation research, because it offers both great technical insights and qualitative understanding of what works and what does not work. A picture or a movie gives an overall, comprehensive view of the system, and can provide information about the source of errors. It gives an immediate view of problems that are otherwise not evident but will show up as features that are out of place or inconsistent with the expected symmetries of the system. This knowledge is further used in deciding where to follow up with code improvement. Other ways students are involved is by doing research on the theoretical understanding of black holes and on the numerical techniques for modeling of black holes collision in the Post-Newtonian approach. The computation of gravitational waves in the post-Newtonian approximation is useful for comparisons with the numerical relativity results.
