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

黑洞，甚至虫洞的抽象概念，如今在公众的视野中非常广泛。例如，最近的电影《星际穿越》（Interstellar）获得了6.727亿美元的票房，而制作预算为1.65亿美元。众所周知，超大质量的旋转黑洞是大多数星系的核心特征。这些奇怪的概念来源于爱因斯坦的引力理论——广义相对论。虽然这个理论已经有100年的历史了，但它仍然是所有现代科学的基石之一，它可能仍然是最具挑战性的科学理论，难以理解和应用。许多例行程序不能靠手工计算可靠地执行。申请人与几名学生一起，在多年的时间里，开发了至今仍被广泛使用的计算机代数系统GRTensor。这个工具基本上可以立即得到结果，否则需要几个月的数学工作。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些专业知识。在广义相对论中，人们解出各种物理情况下的爱因斯坦方程，得到一个叫做时空的解。事实上，第一个解是由史瓦西在1916年发现的，尽管这个解直到1960年才被完全理解。该解表示一个不旋转的球形黑洞。这种理解的延迟是由于GR最弱的方面造成的；需要引入坐标（如球形地球上的经纬度）。研究时空曲率动力学的传统方法在一个非常真实的意义上隐藏了理论的复杂性。无论是庞大的公式，还是海量的数字数据，标准的表达方法都很少使用我们人类在模式识别方面的卓越技能。该研究项目介绍了一种时空曲率可视化的新方法。这个项目已经取得了相当大的成功。例如;我和我的学生们已经揭开了一些90年来一直无法理解的解决方案的物理意义（还有更多的解决方案有待研究），我们已经发展了黑洞体积的概念（不依赖于时空渐近特性的体积，这是一个需要进一步研究的领域），我们已经给出了寻找黑洞视界的坐标独立算法。在这个领域还有很多工作要做，因为我们接近更现实的天体物理情况，比如黑洞的相互作用，以及大宇宙的不太理想的模型。这项研究促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，他们也把自己的才能带到工业界。例如，我最近的毕业生在加拿大庞巴迪运输公司获得了Mitacs加速博士后奖学金**

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.**