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

相对论天体物理学和宇宙学中引力研究的新方法

• 批准号: RGPIN-2016-03628
• 负责人: Lake, Kayll
• 金额: $ 3.64万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=708825
• 关键词: New; approaches; study; gravitation; relativistic

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.

如今，黑洞甚至是虫洞的抽象概念在公众眼中非常重要。例如，最近的电影《星际》（Interstellar）的收入为6.727亿美元，生产预算为1.65亿美元，众所周知，超级大质量旋转的黑洞是大多数星系的主要特征。 这些奇怪的概念来自爱因斯坦的重力理论，一般相对论（GR）。尽管现在有100年历史，但该理论仍然是所有现代科学的基石之一，它仍然可能是最具挑战性的科学理论，可以理解和合作。许多常规过程不能通过手动计算可靠地执行。申请人与几个学生以及多年来都开发了仍然使用的计算机代数系统Grtensor。该工具基本上允许瞬时结果，否则将需要数月的数学工作。我提出的研究计划以结合计算机代数和数值相对论的新方式利用了这种专业知识。在GR中，一个求解了爱因斯坦的方程式，以使各种物理情况得出一个称为时空的溶液。确实，第一种解决方案是由Schwarzschild在1916年发现的，尽管该溶液直到1960年才完全理解。该解决方案代表了一个非旋转的球形黑洞。理解的延迟是GR最弱的结果。需要引入坐标（例如球形地球上的纬度和经度）。在非常真实的意义上研究时空曲率动力学的传统方法隐藏了该理论的复杂性。无论是巨大的公式，还是数值数据的山脉，标准的演示方法几乎不利用我们的非凡技能作为人类，在模式识别上。该研究计划引入了一种新的时空曲率可视化方法。该计划已经取得了巨大的成功。例如;我和我的学生已经阐明了一些解决方案的物理含义，这些解决方案已经避免了90年的理解（还有更多的研究），我们已经开发了黑洞量的概念（不取决于空位的渐近特性，这是一个进一步研究的领域），并且我们已经给出了独立的algorith algorith，可以找到黑洞。当我们处理更现实的天体物理情况时，例如黑洞的相互作用，以及大型宇宙的理想化模型，在这一领域还有很多事情要做。这项研究促进了我们对自然的基本理解，但它也为高素质人员的高级培训提供了独特的机会。我以前的学生不仅在学术界担任高级职位，还将自己的才华带入了行业。例如，我最近的毕业生在加拿大庞巴迪运输公司（Bombardier Transportation Canada Inc.