Theoretical Investigations in Classical and Quantum Gravity

经典和量子引力的理论研究

• 批准号: 1505411
• 负责人: Abhay Ashtekar
• 金额: $ 101.57万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1505411&HistoricalAwards=false
• 关键词: Theoretical; Investigations; Classical; Quantum; Gravity

Recent observations have shown that about 70% of the energy density in the universe cannot be attributed to matter. The simplest explanation of this `dark energy' comes from the cosmological constant that Einstein had initially introduced in his fundamental equations of general relativity. However, for most of the 20th century, it was widely believed that the cosmological constant is zero because all observations were compatible with this simplest possibility. Therefore, the detailed mathematical theories describing the dynamics of compact astronomical objects such as colliding black holes and neutron stars, and gravitational waves they source, was based on this assumption. The goal of the first part of this project is to systematically extend that theory to include a non-zero cosmological constant. The extension will provide a firmer foundation for gravitational wave science. The second part of the project contains studies at the interface of strong gravity and quantum physics. They address fundamental issues related to the quantum evaporation of black holes and the physics of the earliest epoch of our universe when gravity is strong and quantum physics indispensable. The proposed research will have an impact on a broad range of research areas, including general relativity, geometric analysis, cosmology, quantum field theory, and computational science. As a result, through this research, young scientists will be trained in inter-disciplinary science. Currently, these researchers include members of under-represented groups. Through his editorship of series commemorating the centennial of the discovery of general relativity, the PI will commission monographs aimed at communicating the latest advances in science and technology to young researchers. Finally, as in the past, personnel supported by this grant will contribute vigorously to outreach activities through videos, semi-popular articles and public lectures.The first part of the project will address issues arising from the fact that even a tiniest value if the cosmological constant can cast a long shadow on the theory of gravitational waves. As of now, we do not even have a gauge invariant notion of gravitational waves in full, non-linear general relativity with a positive cosmological constant. The goal is to construct a rigorous framework to fill this gap and use it to extract the physics of gravitational waves in a more reliable fashion. The results will open new avenues for analytic and numerical work in the study of the gravitational collapse, compact binary coalescence, energy, momentum and angular momentum emission in such processes, post-Newtonian and post-Minkowskian approximation methods, etc. They are also likely to stimulate research in geometric analysis through new mathematical conjectures (related to positivity of a new notion of energy). The second part of the project will address two types of issues: i) the conceptually fundamental question of whether information is lost in evaporation of black holes; and, ii) the emerging interplay between loop quantum gravity and observations related to the very early universe. This is possible because loop quantum cosmology is now sufficiently mature to make predictions for future observations based on its pre-inflationary dynamics, and to use current observations to seek fundamental principles that presumably dictate the initial conditions for our universe.

最近的观测表明，宇宙中约70%的能量密度不能归因于物质。对这种“暗能量”的最简单解释来自于爱因斯坦最初在他的广义相对论基本方程中引入的宇宙常数。然而，在20世纪的大部分时间里，人们普遍认为宇宙常数为零，因为所有的观测都符合这种最简单的可能性。因此，描述黑洞和中子星碰撞等致密天体的动力学及其产生的引力波的详细数学理论就是基于这一假设。这个项目第一部分的目标是系统地扩展这一理论，将非零的宇宙常数包括在内。这一延伸将为引力波科学提供更坚实的基础。该项目的第二部分包括对强引力和量子物理界面的研究。它们解决了与黑洞的量子蒸发和我们宇宙最早时代的物理学有关的基本问题，当时引力很强，量子物理不可或缺。拟议的研究将对广泛的研究领域产生影响，包括广义相对论、几何分析、宇宙学、量子场论和计算科学。因此，通过这项研究，青年科学家将接受跨学科科学方面的培训。目前，这些研究人员包括代表性不足的群体的成员。通过他担任纪念广义相对论发现一百周年系列的编辑，国际和平协会将委托出版旨在向年轻研究人员交流科学技术最新进展的专著。最后，像过去一样，由这笔赠款资助的人员将通过视频、不太受欢迎的文章和公共讲座积极地为推广活动做出贡献。该项目的第一部分将解决这样一个事实，即即使是最微小的值，如果宇宙常数可能会对引力波理论产生长期的阴影，也会产生问题。到目前为止，我们甚至还没有完整的、具有正宇宙常数的非线性广义相对论中的引力波的规范不变概念。目标是构建一个严格的框架来填补这一空白，并用它以更可靠的方式提取引力波的物理学。这些结果将为分析和数值研究引力崩塌、致密双星合并、这类过程中的能量、动量和角动量发射、后牛顿和后Minkowskian近似方法等开辟新的途径，也可能通过新的数学猜想(与新能量概念的正性有关)来促进几何分析的研究。该项目的第二部分将解决两类问题：i)概念上的基本问题，即信息是否在黑洞的蒸发中丢失；以及ii)环圈量子引力和与非常早期的宇宙有关的观测之间的新的相互作用。这是可能的，因为环圈量子宇宙学现在已经足够成熟，可以根据其膨胀前的动力学对未来的观测做出预测，并利用目前的观测来寻找可能决定我们宇宙初始条件的基本原理。