Theoretical and Numerical Studies in Gravitational Collapse and Relativistic Astrophysics

在引力坍缩、广义相对论中的临界现象和相对论天体物理学中提出了若干理论和数值研究。这个项目的主要重点包括：(1)对最近发现的与广义相对论中引力坍缩相关的关键现象进行积极的研究；(2)对黑洞双星轨道衰变和合并建模的几个步骤进行研究；(3)对日蚀脉冲星和相对论脉冲星风的物理研究；(4)对磁流体动力学（MHD）风和磁约束射流的数值研究。研究临界现象的目标是理解与其他领域（如统计物理学）的临界现象之间的联系，探索崩溃中临界行为的最简单例子的分析性质，并通过数值实验发现临界现象的其他物理上不同的例子。合并黑洞双星的工作目标是在两个空间维度（2+1）中开发和探索黑洞视界内边界条件的使用，并开发有效利用大规模并行架构的算法。在这两种情况下，在2+1中开发的知识将扩展到三个维度（3+1）。对食脉冲星的研究将集中于研究非线性等离子体不稳定性的简单解析/数值模型，这可能与短周期、低质量系统有关，并研究相对论性脉冲星风与正常恒星风之间的相互作用。在上一个拨款期开始的通用MHD代码（AVATAR）将继续发展，用于研究MHD风的自准直和磁约束射流的传播。

Several theoretical and numerical studies are proposed in gravitational collapse, critical phenomena in general relativity and relativistic astrophysics. The major focuses of this program include: (1) a vigorous investigation of the critical phenomena recently discovered to be associated with gravitational collapse in general relativity, (2) an investigation of several steps toward modeling the orbital decay and coalescence of black hole binaries, (3) several investigations of the physics of eclipsing pulsars and relativistic pulsar winds, and (4) numerical studies of magnetohydrodynamic (MHD) winds and magnetically-confined jets. The objectives of work in critical phenomena are to understand the connections to critical phenomena in other areas such as statistical physics, to explore analytic properties of the simplest examples of critical behavior in collapse, and to discover additional, physically-distinct examples of critical phenomena through numerical experimentation. The objectives of work on coalescing black hole binaries are to develop and explore in two spatial dimensions (2+1) the use of an apparent horizon inner boundary condition for black holes and to develop algorithms that efficiently utilize massively-parallel architectures. In both cases, knowledge developed in 2+1 will be extendible to three dimensions (3+1). Work on eclipsing pulsars will focus on investigating simple analytic/numerical models of nonlinear plasma instabilities, which may be relevant for short-period, low-mass systems, and investigating the interaction between relativistic pulsar winds and normal stellar winds. Continued development of a general purpose MHD code (AVATAR), begun in the last grant period, will be pursued, with application to the study of self-collimation of MHD winds and propagation of magnetically-confined jets.