Research in Gravitational Physics

该奖项涉及引力物理学的广泛研究，包括经典广义相对论和弯曲时空中的量子场论的研究项目。这项研究的主要目的是更深入地了解爱因斯坦广义相对论对黑洞现象的影响，以及强引力场中量子现象的性质。研究将涉及研究生直接参与研究的各个方面，从而有助于他们的培训。与该奖项相关的研究领域是公众相当感兴趣的，将开展活动，如举办公开讲座，以帮助向公众传播科学知识。建议的具体研究课题包括：（i）与经典记忆效应相关的量子场红外发散的分析，具体地说，（a）是否可以定义包含记忆的合适的“内”和“外”希尔伯特空间，（B）“软引力子”的退相干效应;（ii）分析量子应力-能量张量是否必须在柯西视界上总是奇异的，从而实施强宇宙审查;（iii）分析相互作用量子场的算符乘积展开是否能得到局部和协变的“流关系”;（iv）分析与之相互作用的量子场的真空涨落对粒子位置测量的限制;（v）分析离散时空模型中的近似庞加莱不变性;以及（vi）一项关于是否以及如何理解数学不适定方程的调查，这些方程旨在代表替代广义相对论的有效场论。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award is concerned with a broad range of research in gravitational physics, including research projects in classical general relativity and quantum field theory in curved spacetime. The main aim of this research is to obtain a deeper understanding of the implications of Einstein's theory of general relativity for phenomena involving black holes, as well as the nature of quantum phenomena in strong gravitational fields. The research will involve the direct participation of graduate students in all aspects of the research, and it will thereby contribute to their training. The areas of research associated with this award are of considerable interest to the public, and activities will be undertaken, such as giving public lectures, that aid in the dissemination of scientific knowledge to the public.The specific research topics proposed include: (i) an analysis of the quantum field infrared divergences associated with the classical memory effect, specifically (a) whether suitable "in" and "out" Hilbert spaces incorporating memory can be defined and (b) the decoherence effects of "soft gravitons"; (ii) an analysis of whether the quantum stress-energy tensor must always be singular on a Cauchy horizon, thereby enforcing strong cosmic censorship; (iii) an analysis of whether local and covariant "flow relations" can be obtained for the operator product expansion of interacting quantum fields; (iv) an analysis of the limitations on position measurements of a particle resulting from vacuum fluctuations of a quantum field with which it interacts; (v) an analysis of approximate Poincare invariance in discrete spacetime models; and (vi) an investigation of whether and how one can make sense of mathematically ill posed equations that are intended to represent effective field theories for alternatives to general relativity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.