Models and Applications of Loop Quantum Gravity

为了探索提出的量子引力理论对空间和时间的影响，研究这些理论对特定时空的影响往往是有用的。对称解和相关模型是这种方法的主要例子之一，其动机是希望从(经典或)量子引力中提取物理信息。虽然已提出的量子引力理论足够复杂，如何构建对称模型并不明显，但已经为当前量子引力理论的候选之一-循环量子重力-开发了几种技术。对于从来不是完全对称的现实情况，将开发出至少包含与对称的微小偏差的更一般的结构，例如空间不均匀。这一推广可能允许计算可能与宇宙学观测相关的量子引力效应或了解黑洞的性质。由于量子引力理论仍在发展中，任何关于可能候选者行为的信息，特别是在物理场景中的信息，都将有助于指导理论构建。反过来，人们普遍认为量子引力对于从根本上理解宇宙是必不可少的。这尤其适用于简化的宇宙学和黑洞这两个主要应用领域，这两个领域也受到公众的广泛关注。该项目开发的模型能够进行直观的解释，从而使如此广泛的传播成为可能。在简化复杂的完整理论的过程中，合适的模型也为新进入该领域的学生或研究人员提供了理想的切入点。

In order to explore the implications of proposed theories of quantum gravity for space and time, it is often useful to study the theories' effects for special space-times. Symmetric solutions and related models present one of the main examples of this approach, motivated by the wish to extract physical information from (classical or) quantum gravity. While proposed quantum gravity theories are sufficiently complex that how to construct symmetric models is not obvious, several techniques have been developed for one of the current candidates for a quantum theory of gravity, loop quantum gravity. For realistic situations, which are never exactly symmetric, more general constructions containing at least small deviations from symmetry such as spatial inhomogeneities will be developed. This generalization may allow calculation of quantum gravity effects which might be relevant to cosmological observations or to understand properties of black holes.Since quantum theories of gravity are still being developed, any information on the behavior of possible candidates, in particular in physical scenarios, will help to guide the theoretical construction. Quantum gravity, in turn, is widely believed to be essential for the understanding of the universe at a fundamental level. This applies in particular to the two main areas of application of application of the simplified, cosmology and black holes, which also receive wide interest in the general public. Models as developed by this project enable intuitive explanations which make such a broad dissemination possible. In simplifying the complex full theories, suitable models also provide ideal entry points for students or researchers new to the field.