Singularity Resolution in Quantum Gravity

如果不解决经典引力中的奇点问题，就不可能完全理解我们宇宙的历史。奇点，如大爆炸，是经典空间和时间的边界，经典物理学止步于此。这些奇点表明，潜在的理论，在这里是爱因斯坦的广义相对论，已经达到了其有效性的极限。因此，宇宙诞生等基本问题的答案不能用广义相对论得到，广义相对论是建立在经典的时空概念基础上的。人们预计，量子引力理论将揭示新的物理学，为奇点的解析提供重要线索。在这项研究中，圈量子引力被用来探索不同时空中奇点的命运，包括宇宙学和黑洞时空。从这些研究中得到的教训对于理解时空的量子本质、宇宙早期的物理学以及引力崩塌的最后阶段将是重要的。在这个项目中开展的研究涉及各向同性、各向异性、黑洞和非均匀时空的解析、唯象和数值研究，以了解使用循环量子引力技术的奇点分辨。通过系统地研究这些时空的量子化及其与有效描述的关系，将提取普朗克尺度上的精确物理，并探索其现象学意义。这项研究还旨在解决与量子宇宙中事件的量子概率有关的基本问题，例如量子反弹。这些研究有望为量子引力中奇点的类属解析提供有价值的见解。

A complete understanding of the history of our universe is not possible without addressing the problems of singularities in classical gravity. Singularities, such as the big bang, are the boundaries of classical space and time where the classical physics stops. These singularities signal that the underlying theory, in this case Einstein's theory of General Relativity, has reached its limit of validity. Answers to fundamental questions such as the birth of the universe thus cannot be obtained using general relativity which is based on the classical notion of space and time. It is expected that a quantum theory of gravity would reveal new physics which provides important clues on the resolution of singularities. In this research, loop quantum gravity is used to explore the fate of singularities in different spacetimes, including cosmological and black hole spacetimes. Lessons from these investigations will be important to understand the quantum nature of spacetime, the physics of the very early universe and the final stages of the gravitational collapse. Research carried out in this project deals with analytical, phenomenological and numerical investigations of isotropic, anisotropic, black hole and inhomogeneous spacetimes to understand singularity resolution using techniques of loop quantum gravity. By a systematic study of quantization of these spacetimes and its relation with the effective descriptions, precise physics at the Planck scale will be extracted and phenomenological implications will be explored. This research also aims to address fundamental issues pertaining to the quantum probabilities for events, such as the quantum bounce, in a quantum universe. These investigations are expected to give valuable insights on the generic resolution of singularities in quantum gravity.