New approaches to the study of gravitation in relativistic astrophysics

相对论天体物理学中引力研究的新方法

• 批准号: 8279-2011
• 负责人: Lake, Kayll
• 金额: $ 2.7万
• 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: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=474366
• 关键词: New; approaches; study; gravitation; relativistic

The applicant, along with several students and over a period of many years, developed the widely used computer algebra system GRTensor, an essential tool in the area of applied differential geometry. My proposed research program makes use of this expertise in new ways. Here I will concentrate on just one aspect of this program, gradient fields of curvature. Our work involves the novel use of both computer algebra and numerical routines with the objective being the development of a fresh view of "curvature" - a view that reveals detailed structure and insights previously unavailable. Given any invariant, one can always construct the associated gradient field and study the resultant flow. Essentially, we have turned the abstract idea of curvature into a hypothetical fluid the properties of which can be easily visualized. Although this research is in its early stages, I can already cite the following: (i) The flow distinguishes different types of singularities. For example, whereas the flow seeks out the singular ring in the equatorial plane of the Kerr metric (the real singularity), the flow completely ignores "shell focusing singularities", substantiating my claim, made many years ago, that such singularities are not "gravitational". (ii) In the area of inhomogeneous cosmology, it has been incorrectly claimed that the divergence of the "d'Alembertian of the Ricci scalar" signifies a "weak singularity". Such a divergence is actually a caustic in the gradient flow - and artificial singularity of no consequence. We expect that this fresh approach to the visualization of curvature will evolve into a standard approach much to the benefit to all researchers in the field. Whereas much work remains to be done, one way to summarize this approach is to note that when Killing vectors (directions of symmetry) are available, it is wise to make use of them. Gradient flows are, by construction, orthogonal to Killing flows and are always available - algorithmically. It should be noted that the use of gradient flows is not restricted to Einstein's theory nor to four dimensions. This aspect of my overall research program offers exceptional opportunities for the training of HQP and involves two graduate students and a summer research assistant.

申请人与几个学生以及多年来，开发了广泛使用的计算机代数系统GRTENSOR，这是应用差异几何区域中必不可少的工具。 我提出的研究计划以新的方式利用了这种专业知识。在这里，我将仅专注于该程序的一个方面，即曲率的梯度领域。我们的工作涉及计算机代数和数值例程的新颖使用，目的是开发“曲率”的新视图 - 这种观点揭示了以前无法使用的详细结构和见解。鉴于任何不变，人们总是可以构建相关的梯度场并研究所得流量。从本质上讲，我们将曲率的抽象思想转变为一种假设的流体，其特性可以很容易地可视化。尽管这项研究处于早期阶段，但我已经可以引用以下内容：（i）流动区分了不同类型的奇点。例如，尽管流动在Kerr公制的赤道平面（真正的奇异性）中寻找奇异的环，但流动完全忽略了“壳焦点奇异性”，证明了我的主张，这是多年前提出的，但这种奇异性不是“引力”。 （ii）在不均匀的宇宙学领域，错误地认为，“ Ricci标量的D'Anembertian”的差异表示“弱奇异性”。这种差异实际上是梯度流中的苛刻性，而人为的奇异性没有任何后果。我们预计，这种曲率可视化的新方法将发展成为一种标准方法，从而为该领域的所有研究人员带来了很多好处。尽管还有许多工作要做，但总结这种方法的一种方法是指出，当杀死向量（对称的指示）可用时，使用它们是明智的。通过构造，梯度流是杀死流量的正交的，并且总是可用的 - 算法。 应该注意的是，梯度流的使用不仅限于爱因斯坦的理论，也不限于四个维度。我的整体研究计划的这一方面为HQP培训提供了出色的机会，并涉及两名研究生和一名夏季研究助理。