Problems in numerical relativity

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In the hundred plus years since it was formulated, Einstein's theory of relativity has profoundly impacted our understanding of the role of gravity in the universe. The theory makes absolutely spectacular predictions including the existence of gravitational waves and black holes, and the expansion of the universe. Although it has passed every experimental and observational challenge to which it has been subjected, many unanswered questions about the theory's implications for physics remain, especially when gravity is very strong. At a theoretical level, my primary research field---numerical relativity---uses powerful computer simulations to provide answers to some of these questions. The proposed research will address a variety of issues in strong field gravity. These include: (1) the nature of so-called critical gravitational collapse, where the process of black hole formation is seen to exhibit many features of a phase transition (2) the stability of a particular type of universe, known as anti-de Sitter spacetime, which is of particular interest to string theorists (3) the properties of a newly discovered model for a star-like object with strong gravitational fields and (4) the possibility of using machine learning and other artificial intelligence techniques to efficiently solve the equations we use to model the gravitational interaction. All of this research will be computationally driven. As is the case in many other fields of modern science, such as meteorology, climatology and fluid dynamics, the complexity of Einstein's equations for the gravitational field means that it is only with significant computer power and advanced algorithms that we can make progress in accurately deducing what those equations have to say about many of the situations of most interest. Thus, much of the day-to-day work of the proposed research activities will involve the design and implementation of computer codes to simulate the physical scenarios sketched above. Results of this research will contribute to our fundamental understanding of the gravitational interaction. The work will be important to those working in the fields of gravity, string theory, astrophysics, cosmology and applied mathematics. Training of students at undergraduate and graduate levels, as well as postdoctoral fellows will be a crucial aspect of the research program. Trainees will become expert in formulating and solving complex problems using advanced information technology, allowing them to become key contributors to Canada's increasingly knowledge-based economy.