Research in General Relativity and Gravitation

有一些重要的问题涉及到非常微小尺度上的引力--量子引力占主导地位的尺度--因此，它们隐含地提出了时空最终是连续的还是离散的这个先决问题。 无论这里的答案是什么，时空的离散模型都是出于实际原因而需要的：计算机模拟将告诉我们如何解释来自LIGO等引力波望远镜的数据。 这项研究将在这一广泛框架内探讨以下具体专题。 这些方法既可以是分析的（纸笔计算和推导），也可以是数值的（计算机模拟）。 黑洞的性质：黑洞的表面（它的“视界”）是否具有牛顿分析所指出的“分形”结构？ 离散时空：进一步发展Regge演算作为数值求解爱因斯坦方程的实用工具;进一步发展因果集理论，专注于局部性和宇宙常数的问题。 时空拓扑和拓扑变化：拓扑几何的性质是什么？当它们被创造和毁灭时会发生什么？ 量子宇宙学：因果集合论所指出的随时间变化的宇宙学常数的观测效应是什么？ 量子力学的历史求和方法：我们如何在引力存在的情况下继续用量子力学进行预测？

There are important questions which refer to gravity on very tiny scales--scales where quantum gravity reigns--and therefore they implicitly raise the prior question whether spacetime is ultimately continuous or discrete. No matter what the answer here, discrete models of spacetime are needed for practical reasons: for the computer simulations which will tell us how to interpret the data coming from gravitational wave telescopes like LIGO. This research would address the following specific topics within this broad framework. The methods would be both analytic (paper and pencil computations and derivations) and numerical (computer simulations). properties of black holes: does the surface of the black hole (its `horizon`) possess a `fractal` structure, as Newtonian analysis indicates? discrete spacetime: further development of Regge Calculus as a practical tool for solving the Einstein equations numerically; further development of causal set theory, focusing on the issues of locality and the cosmological constant. spacetime topology and topology-change: what are the properties of topological geons and what happens when they are created and destroyed? quantum cosmology: what are the observational effects of the time varying cosmological constant indicated by causal set theory? sum-over-histories approach to quantum mechanics: how can we continue to make predictions with quantum mechanics in the presence of gravity?