Theoretical Investigations in Classical and Quantum Gravity

一些理论引力物理学的项目将被完成。在第一组中，与黑洞有关的问题将使用Ashtekar小组最近引入的新范式进行分析。 特别是，物理信息将从引力如此强大以至于爱因斯坦广义相对论效应占主导地位的区域的黑洞合并的数值模拟中提取。在第二组中，与爱因斯坦广义相对论的结构和解决方案有关的数学问题将使用罗杰·彭罗斯介绍并由他的研究小组开发的“扭曲理论”来解决。第三组包含了一些与量子引力有关的项目，该理论将统一广义相对论和量子物理学。Ashtekar和Pullin的研究小组将开发合适的近似方法，以更好地理解量子引力理论的结构，这是由PI和其他人开发的，并做出可以在不久的将来进行测试的物理预测。这些项目将几个领域联系起来：广义相对论，计算物理学，天体物理学，量子理论和几何学的几个分支。例如，第一组项目是基于爱因斯坦的广义相对论方程，但对最终黑洞的质量和自旋以及在此过程中辐射的能量的准确估计，将对一般的天体物理学，特别是引力波物理学产生影响。第二组将使用代数几何的新技术来解决爱因斯坦方程。广义相对论与量子物理的统一可能是当今基础物理学中最突出的未解决问题。第三套计划中的项目将联合收割机结合现代数学和理论物理学的尖端技术，在当今可以想象的最小尺度上探索时空几何的本质。通过广义相对论，爱因斯坦提出几何是一个物理实体。 我们的一些项目旨在将爱因斯坦的视野提升到量子世界，特别是表明物质，辐射和几何可以通过涉及引力的量子过程相互转换。 其他项目将利用正在进行的NASA任务对伽马射线爆发的天文观测，直接探测这些新量子效应的热效应。这将是第一次系统性的努力，用具体的实验来对抗相当抽象的量子引力理论。

A number of projects in theoretical gravitational physics will becompleted. In the first set, issues pertaining to black holes will beanalyzed using a new paradigm, introduced recently by Ashtekar'sgroup. In particular, physical information will be extracted fromnumerical simulations of black hole mergers in regions where gravityis so strong that effects of Einstein's general relativity dominate.In the second set, mathematical issues pertaining to the structure andsolutions of Einstein's general relativity will be resolved using``Twistor theory'' introduced by Roger Penrose and developed by hisresearch group. The third set contains a number of projects pertainingto quantum gravity, the theory that will unify general relativity withquantum physics. Suitable approximation methods will be developed bythe research groups of Ashtekar and Pullin to better understand thestructure of a quantum gravity theory, that is being developed by thePIs and others, and to make physical predictions which could be testedin the near future.These projects interlink several fields: general relativity,computational physics, astrophysics, quantum theory and severalbranches of geometry. For example, the first set of projects is basedon Einstein's equations of general relativity but the accurateestimates of the mass and spin of the final black hole and of theenergy radiated in the process, obtained from them, will have impacton astrophysics in general and to gravitational wave physics inparticular. The second set will use novel techniques from algebraicgeometry to solve Einstein's equations. Unification of generalrelativity and quantum physics is perhaps the most outstanding openproblem in fundamental physics today. The proposed projects in thethird set combine sophisticated techniques from modern mathematics andtheoretical physics to probe the nature of space-time geometry at thesmallest scales conceivable today. Through his general relativitytheory, Einstein proposed that geometry is a physical entity. Some ofour projects are aimed at elevating Einstein's vision to the quantumworld showing, in particular, that matter, radiation and geometry canbe converted in to one another through quantum processes involvinggravity. Other projects will use astronomical observations of gammaray bursts from ongoing NASA missions to directly probe theramifications of these novel quantum effects. This will be among thefirst systematic efforts at confronting the rather abstract quantumgravity theory with concrete experiments.