Problems in numerical relativity

爱因斯坦的广义相对论，也就是现代引力理论，深刻地影响了我们对宇宙的理解。它做出了绝对壮观的预测，例如宇宙的扩张和黑洞的存在。尽管它已经通过了无数的实验测试，但关于它的有效性和对物理学的影响，仍然有许多悬而未决的问题。利用强大的计算机模拟，这项拟议的研究将回答其中一些问题。 可以肯定的是，在某些情况下，爱因斯坦的理论需要修改以提供对现实的准确描述。因此，人们正在积极研究广义相对论的许多扩展和修改。对恒星和黑洞的模拟将评估这些替代方案的可行性。弦理论旨在将广义相对论与量子力学结合在一起，它要求宇宙具有超过三个空间维度：对黑洞形成的模拟将提供对这一迷人想法的洞察。此外，在某些情况下，黑洞的形成方式与物质状态的转变非常相似，比如液态水在沸腾时会发生什么。这一现象也将得到调查。 这项研究的结果将有助于我们对引力的基本理解，并对我们在最大和最小尺度上的宇宙观产生影响。这项工作对重力、弦理论、天体物理学、宇宙学和应用数学领域的人来说将是重要的。对各级学生的培训将是不可或缺的。他们将成为使用计算机技术解决复杂问题的专家。这将使他们成为加拿大日益以知识为基础的经济的许多部门的关键贡献者，包括高等教育、软件工程、电信、金融和国防。

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.