CAREER: Explorations in Quantum Gravity: Cosmological and Black Hole Spacetimes

在爱因斯坦的广义相对论中，经典时空终止于奇点。例子包括宇宙学模型中的大爆炸奇点和黑洞时空的中心奇点。在这些事件中，时空曲率和潮汐力变得无限大。经典进化停止了。人们一直希望量子引力效应能为解决这个基本问题提供见解。这个教师早期职业奖支持研究，以回答有关量子引力和宇宙学和黑洞时空奇点的分辨率的各种问题。在这个项目中进行的研究将使用圈量子引力技术。一个主要的目标是建立量子时空在各向异性和不均匀性存在下的一般性质，并提取可靠的现象学和观测预测。该项目的教育和外联目标旨在面向广大受众。该项目旨在通过一系列公开讲座和科学展览和示范，加强K-12学生的科学知识。积极参与技术将用于改进本科生和研究生课程。本科生和研究生也将通过研究活动接受培训。将探索不同模型中奇点分辨率对物理的详细影响。该项目旨在大大拓宽和推进我们目前对量子引力物理学的理解。研究探索将包括（i）系统地研究不同时空的量子化及其产生的物理学，包括Gowdy模型和Schwarzschild黑洞中的各向异性和不均匀性;（ii）通过分析量子引力对宇宙学扰动的影响来提取唯象意义;以及（iii）使用一致历史方法解决量子宇宙学的基本问题。在这个项目中开发的数值技术也将导致对经典引力结果的新见解，例如经典奇点附近的时空结构。

In Einstein's theory of general relativity classical spacetime ends at the singularities. Examples include the Big Bang singularity in cosmological models and the central singularity of the black hole spacetimes. At these events the spacetime curvature and tidal forces become infinite. Classical evolution stops. It has been hoped that quantum gravitational effects will provide insights on resolution of this fundamental problem. This Faculty Early CAREER award supports research towards answering various questions related to quantum gravity and resolution of singularities in cosmological and black hole spacetimes. The research carried out in this project will use techniques of loop quantum gravity. A primary objective will be to establish generic properties of quantum spacetime in presence of anisotropies and inhomogenities, and extract reliable phenomenological and observational predictions. The educational and outreach objectives of this project are designed to address a wide audience. The project aims to enhance the scientific enrichment of K-12 students via a public lecture series and science exhibitions and demonstrations. Active engagement techniques will be used to revamp undergraduate and graduate courses. Undergraduate and graduate students will also receive training through research activities.Detailed implications of the singularity resolution on the physics in different models will be explored. The project aims to significantly broaden and advance our current understanding of the physics of quantum gravity. Research explorations will include (i) systematically investigating the quantization and resulting physics of different spacetimes including anisotropies, inhomogenities in Gowdy models and Schwarzschild black holes, (ii) extracting phenomenological implications by analyzing effects of quantum gravity on cosmological perturbations, and (iii) addressing fundamental issues in quantum cosmology using consistent histories approach. Numerical techniques developed in this project will also lead to fresh insights on results in the classical gravity, such as on the structure of spacetime near classical singularities.