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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=633177
• 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，甚至虫洞的抽象概念如今已广泛出现在公众的视野中。例如，最近的电影《星际穿越》的制作预算为 1.65 亿美元，但其票房收入为 6.727 亿美元，众所周知，超大质量旋转黑洞是大多数星系的中心特征。这些奇怪的概念源自爱因斯坦的引力理论——广义相对论（GR）。尽管这一理论已有 100 年的历史，但它仍然是所有现代科学的基石之一，并且它仍然可能是理解和使用时最具挑战性的科学理论。许多常规程序无法通过手工计算可靠地执行。申请人与几名学生一起，经过多年的努力，开发了至今仍广泛使用的计算机代数系统 GRTensor。该工具基本上可以即时得出结果，否则需要花费数月的数学工作。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这些专业知识。在广义相对论中，人们可以针对各种物理情况求解爱因斯坦方程，从而得出称为时空的解。事实上，第一个解是由史瓦西 (Schwarzschild) 于 1916 年发现的，尽管该解直到 1960 年才被完全理解。该解代表一个不旋转的球形黑洞。这种理解上的迟缓是由于 GR 最薄弱的方面造成的。需要引入坐标（例如球形地球上的纬度和经度）。真正意义上的时空曲率动力学研究的传统方法隐藏了理论的复杂性。无论是庞大的公式，还是大量的数字数据，标准的表示方法都很少利用我们人类在模式识别方面的卓越技能。该研究项目引入了一种时空曲率可视化的新方法。该计划已经取得了相当大的成功。例如;我和我的学生们解开了一些近 90 年来一直无法理解的解的物理意义（还有更多的解有待研究），我们提出了黑洞体积的概念（不依赖于时空渐近性质的体积，这是一个需要进一步研究的领域），并且我们给出了寻找黑洞视界的与坐标无关的算法。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，以及不太理想化的大宇宙模型，在这一领域还有很多工作要做。这项研究增进了我们对自然的基本认识，同时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，还将他们的才华带到了工业界。例如，我最近的毕业生拥有庞巴迪运输加拿大公司的 Mitacs Accelerate 博士后奖学金。