Statistical Mechanics in General Relativity and Gravitational Physics

近年来，非平衡统计力学和动力系统理论在相对论天体物理和量子场论中的应用越来越多。坎德鲁普教授将调查其中许多应用程序背后的某些一般特征，并展示此类调查如何为具体问题提供重要的新见解。另一个需要考虑的领域是早期宇宙中统计物理学和量子场论思想的应用。统计力学中要考虑的一个主要领域是经典恒星自引力系统的“松弛”和稳定性。需要解决的相关问题包括：当星系的名义弛豫时间比宇宙年龄大得多时，为什么它们看起来彼此如此相似，并且如此松弛？由于自引力质点系统的“混合”性质，这种表观弛豫能从第一性原理中得到吗？与“碰撞”弛豫时间相比，“平均场涨落”或其他集体效应能否在较短的时间尺度上引起有效的驰豫？在什么意义上，所有的自引力系统都是不稳定的，这种普遍的不稳定会导致在星系中心形成一个大质量黑洞吗？在场论中需要解决的相关问题包括：早期宇宙中的各种场论过程在多大程度上可以用简单的随机方程来建模？所谓的“引力熵”是什么意思？我们能把半经典量子引力中的拓扑变化想象成以瞬子为特征的“隧穿”事件吗？例如，人们能否准确地认为宇宙是通过隧道形成的，是一种量子涨落？这意味着大爆炸的“初始条件”是什么？这能“解释”观测到的“时间之箭”吗？

Recent years have witnessed increasing applications of nonequilibrium statistical mechanics and dynamical systems theory in relativistic astrophysics and quantum field theory. Professor Kandrup will investigate certain general features underlying many of these applications and show how such investigations can provide significant new insights into specific problems. The other area to be considered entails an application of ideas from statistical physics and quantum field theory in the early Universe. One principal area in statistical mechanics to be considered is the "relaxation" and stability of classical self-gravitating systems of stars. Relevant questions to be addressed include: Why do galaxies look so similar one to another and "so relaxed" when their nominal relaxation time is much greater than the age of the Universe? Can this apparent relaxation be derived from first principles as a consequence of the "mixing" properties of a system of self-gravitating point masses? Could "mean field fluctuations" or other collective effects induce an effective relaxation on a time scale short compared with the "collisional" relaxation time? In what sense are all self-gravitating systems unstable, and could this generic instability lead to the formation of a massive black hole at the center of a galaxy? Relevant questions to be addressed in field theory include: To what extent can various field theoretic processes in the early Universe be modeled via simple stochastic equations? What does one mean by "gravitational entropy"? Is it possible to envision changes in topology in semiclassical quantum gravity as "tunneling" events, characterized as instantons? Could one, e.g., make precise the idea that the Universe "tunneled into Being" as a quantum fluctuation? What would this imply about the "initial conditions" at the Big Bang, and could this "explain" the observed "arrow of time"?