Theoretical Investigations in Classical and Quantum Gravity

经典和量子引力中的基本概念和数学问题将被研究，以丰富我们对爱因斯坦广义相对论的理解并超越它。具体来说，将探索早期宇宙的物理学，分析大爆炸的量子性质，研究黑洞的热力学和量子性质。在引力物理和几何界面上的其他问题也将被研究，包括在奇点附近的物质密度和曲率变得无限的广义相对论的完全非线性制度，以及经典物理学的终结。因为重点是在引力物理学的前沿问题，研究生和博士后将继续接受广泛的培训，这将对他们的职业生涯产生长期影响。这项工作的结果将通过以下方式丰富其他学科：1)为宇宙学提供新的输入；Ii)在非交换几何方面取得新进展；Iii)发展计算量子宇宙学领域；（四）向更广泛的公众传播前沿科学研究。

Fundamental conceptual and mathematical issues in classical and quantum gravity will be investigated to enrich our understanding of Einstein's general relativity and to go beyond. Specifically, the physics of the early universe will be explored, the quantum nature of the Big Bang will be analyzed, and thermodynamic and quantum properties of black holes will be studied. Other issues at the interface of gravitational physics and geometry will also be investigated, including the fully non-linear regime of general relativity near singularities at which matter density and curvature become infinite, and classical physics comes to an end.Because the emphasis is on issues at the forefront of gravitational physics, graduate students and post-docs will continue to receive broad training that will have a long-term impact on their careers. Results of this work will enrich other disciplines by: i) providing novel inputs to cosmology; ii) making a new advance in non-commutative geometry; iii) developing the area of computational quantum cosmology; and, iv) disseminating frontier scientific research to the broader public.