New approaches to the study of gravitation in relativistic astrophysics and cosmology

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The abstract concept of a black hole, or even a wormhole, is nowadays very much in the public eye. For example, the recent film Interstellar has produced earnings of $672.7 million against a production budget of $165 million, and it is common knowledge that supermassive rotating black holes are the central feature of most galaxies. These bizarre concepts arise from Einstein’s theory of gravity, General Relativity (GR). Though now 100 years old, this theory remains as one of the cornerstones of all modern science, and it remains perhaps the most challenging scientific theory to understand and to work with. Many routine procedures cannot be executed reliably by hand calculation. The applicant, along with several students, and over a period of many years, developed the still widely used computer algebra system GRTensor. This tool allows essentially instantaneous results that would otherwise take months of mathematical work. My proposed research program makes use of this expertise in new ways that combine computer algebra and numerical relativity. In GR one solves Einstein’s equations for various physical situations to arrive at a solution called a spacetime. Indeed, the first solution was found in 1916 by Schwarzschild though the solution was not fully understood until 1960. The solution represents a non-rotating spherical black hole. This delay in understanding was the result of the weakest aspect of GR; the need to introduce coordinates (like latitude and longitude on a spherical Earth). Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the theory. Whether it be huge formulas, or mountains of numerical data, standard methods of presentation make little use of our remarkable skill, as humans, at pattern recognition. The research program introduces a new approach to the visualization of spacetime curvature. The program has already seen considerable success. For example; my students and I have unraveled the physical meaning of some solutions that have avoided understanding for some 90 years (and many more are to be studied), we have developed the concept of black hole volumes (volumes that do not depend on the asymptotic properties of spacetimes, an area of much further study), and we have given coordinate independent algorithms that find black hole horizons. There is much left to be done in this area as we approach more realistic astrophysical situations, such as the interaction of black holes, and less idealized models of the Universe in the large. This research advances our fundamental understanding of nature, but it also provides unique opportunities for the advanced training of highly qualified personnel. My former students not only hold advanced positions in academia, they also bring their talents to industry. For example, my most recent graduate holds a Mitacs Accelerate Postdoctoral Fellowship at Bombardier Transportation Canada Inc.