Problems in numerical relativity

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Einstein's theory of general relativity, the modern theory of gravity, has profoundly impacted our understanding of the universe. It makes absolutely spectacular predictions, such as the expansion of the cosmos and the existence of black holes. Although it has passed a myriad experimental tests, there remain many unanswered questions about its validity and consequences for physics. Using powerful computer simulations, the proposed research will answer some of these questions. It is certain that there are circumstances where Einstein's theory will need alteration to provide an accurate description of reality. Thus, many extensions and modifications of general relativity are being studied vigorously. Simulations of stars and black holes will assess the viability of these alternatives. String theories, which aim to wed general relativity with quantum mechanics, require the universe to have more than three spatial dimensions: simulations of black hole formation will provide insight into this fascinating idea. Moreover, the way that black holes form in some cases is remarkably similar to a transition in the state of matter, such as what happens to liquid water when it boils. This phenomenon will also be investigated. Results of this research will contribute to our fundamental understanding of gravity, with implications for our view of the universe on both the largest and smallest scales. The work will be important to those in the fields of gravity, string theory, astrophysics, cosmology and applied mathematics. Training of students at all levels will be integral. They will become expert in the use of computer technology to solve complex problems. This will allow them to be key contributors in many sectors of Canada's increasingly knowledge-based economy, including higher education, software engineering, telecommunications, finance, and defense.