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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=656398
• 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.**

黑洞的抽象概念，甚至是虫洞，如今在公众的视线中非常普遍。例如，最近的电影《星际穿越》在1.65亿美元的制作预算下创造了6.727亿美元的收入，众所周知，超大质量旋转黑洞是大多数星系的中心特征。这些奇怪的概念源于爱因斯坦的引力理论--广义相对论。尽管现在已经有100年的历史了，这一理论仍然是所有现代科学的基石之一，而且它可能仍然是理解和使用最具挑战性的科学理论。许多常规程序不能靠手工计算可靠地执行。申请者与几名学生一起，在多年的时间里开发了至今仍在广泛使用的计算机代数系统GR。这个工具基本上可以即时得出结果，否则就需要几个月的数学工作。我提议的研究计划以新的方式利用这种专业知识，将计算机代数和数值相对论结合起来。在《GR》中，人们求解爱因斯坦方程，得到一种称为时空的解。事实上，第一个解决方案是在1916年由Schwarzschild发现的，尽管这个解决方案直到1960年才被完全理解。该解代表一个不旋转的球面黑洞。这种理解上的延迟是GR最弱的方面的结果；需要引入坐标(如球面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掩盖了该理论的错综复杂。无论是庞大的公式，还是堆积如山的数字数据，标准的表示方法几乎没有利用我们作为人类在模式识别方面的非凡技能。该研究项目介绍了一种新的时空曲率可视化方法。该项目已经取得了相当大的成功。例如，我和我的学生已经解开了一些解决方案的物理意义，这些解决方案在大约90年的时间里一直不被理解(还有更多的有待研究)，我们发展了黑洞体积的概念(与时空的渐近性质无关的体积，这是一个进一步研究的领域)，我们给出了寻找黑洞视界的坐标独立算法。随着我们接近更现实的天体物理情况，例如黑洞的相互作用，以及不那么理想化的宇宙模型，在这一领域还有很多工作要做。这项研究促进了我们对自然的基本认识，但也为高素质人才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，他们还将自己的才华带到了行业中。例如，我最近毕业的学生在庞巴迪加拿大运输公司获得了Mitacs Accelerate博士后奖学金**