Taylor Hugh Morgan and David Neilsen, Department of Physics and Astronomy
I. Introduction Our research is on the gravitational three-body problem where there are three star-like objects with the only acting force on the objects being gravity. Since the discovery of gravity, many physicists and mathematicians have looked for an analytic solution to the three-body problem including Poincare, Euler, Lagrange, and Jacobi. We now know that there is in fact no analytic solution to this problem. Due to the advent of high performance computing we have discovered much about the chaotic nature1 of this problem and its sensitivity to initial perturbations. For our research we have extended the scope of the three-body problem to general relativity. Our hope for this research is to understand how multiple body systems and general relativity affect black hole formation in regions like galactic centers.
II. Methodology Because of the nature of this problem we have utilized high performance computing, specifically the Marylou supercomputer. My involvement in this process involved several main duties: – Create code that would utilize physics principles to generate the initial conditions for big simulations – Submit and manage these massive jobs (our simulations tended to use 1024 processors at a time and took several hours to several days). – Create tools to analyze the data and visualize the output – Document the steps I took and write a journal entry The figures below show some of the visualizations and setups that were part of what I did.
III. Results We found in our simulations that all of the methods resulted in regions of chaos (the static) and regions of stability (solid color). These regions are most prominent in the Newtonian and PPN2 approximation (The regions that look like static are called “chaotic” because an infinitesimal change in the initial conditions results in a completely different result). We also recognize the abundance of black hole formations in the case with gravitational radiation and the lack of chaotic regions. This can be explained by the fact that most of these chaotic regions involve very close approaches of at least two of the bodies. The power that is lost due to gravitational radiation is by a factor of 1/r^5, so the closer the approach the more power lost. Thus the chaotic regions result in at least two of the bodies spiraling into black holes.
IV. Discussion and Conclusions Our results indicate that gravitational radiation and multiple body systems result in frequent black hole formations. Thus this may be a possible explanation for why there 1 See Boyd and McMillian’s Chaotic Scattering in the Gravitational Three-Body Problem is such an abundance of supermassive black holes in the universe. Future research that relate more directly to galactic centers would involve multiple body systems. A noteworthy mention is we have written and are submitting a journal article due to this research. On top of this I have presented this research at APS four corners meeting two years in a row. I have also presented at BYU’s spring research conference and will be presenting next year. I am very grateful for the funds provided by ORCA. They have helped me immensely.