Understanding complicated gravitational physics by simple two-shell systems

本项目旨在通过简单模型来理解复杂的引力物理。引力中一些有趣且基本的问题，例如黑洞临界现象、从黑洞中提取能量、以及虫洞的非线性稳定性，由于引力的非线性很难被解决。然而，我们可以从一些简单的理想模型获得新的见解。首先，我将介绍了关于无限薄物质的概念，即所谓的“壳”。它是一种在引力中使用广泛的简单系统。我将阐明壳系统在解决上述基本问题起到的重要作用。其次，作为壳系统的进一步应用，我将进一步介绍所谓的“双壳系统”。该系统具有许多非线性物理特性。通过双壳系统，我们可以合理地研究非线性物理中的复杂问题。该系统在解决引力中尚未解决的问题方面也有多种应用。然而，尽管双壳系统存在潜在的解决引力中复杂问题的可能性，此前很少有关于双壳系统数值方法的研究。因此，研究双壳系统的最一般的形式，开发相应的数值计算代码，并将该代码应用于许多物理系统以遵循非线性演化显得十分重要。基于此，我将采用双壳系统解决上述基本问题。

My purpose is to understand complicated gravitational physics by simple models. Due to the nonlinearity of the Einstein equations, gravitational physics sometimes involves intense numerical calculations to follow the co-evolution of matters and spacetimes. These are interesting and fundamental problems in gravitational physics: (1) BH critical phenomena, (2) Extraction of energy from BHs, and (3) Nonlinear stability of wormholes. The status of these studies is explained and related open issues will be introduced. These fundamental problems, however, are not easy tasks to approach because nonlinearity of gravity deeply contribute to these physics. In physics, many insights can be frequently obtained from simple and idealized models. I introduce the concept of an infinitely thin layer of matter, a so-called “shell”, that is a very simple system often used in gravitational physics. I also explain how the shell system are useful and shed light on fundamental problems. After that, I will introduce a simple configuration system called "two-shell system" as a further application of the shell system. This system is very simple, yet exhibits a lot of nonlinear physics, which makes the two-shell system very attractive. With this system, one can study complicated problems of nonlinear physics in a reasonably accessible way. Also, the simple two-shell system have various application to approach unsolved problems in gravitational physics. However, in spite of the potential possibility, there are a very little number of previous studies on the numerical approach of the two-shell system, even though numerical investigations on this system have revealed rich gravitational physics lurking therein. Thus, many applications and possibilities remain unexplored in the two-shell system. Surprisingly, the two-shell system can treat the fundamental gravitational physics problems described above. Therefore, it is important to formulate the most general form of the two-shell system, develop corresponding numerical code, and apply the code to many physical systems to follow nonlinear evolution. Under this situation, I adopt the two-shell system and approach the main problems (1), (2) and (3) mentioned above. All of these problems can be treated by using the two-shell system in a consistent way. It is described in this application that a detailed project for setting and answering 15 open questions related to these 3 main problems ((1) - (3)).