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一些理论和数值研究。 该计划的主要重点包括：（1）对最近发现的与广义相对论中的引力坍缩有关的关键现象进行了有力的调查，（2）对模拟黑洞双星的轨道衰变和合并的几个步骤进行了调查，（3）对食双星和相对论脉冲星风的物理学进行了几项调查，（4）磁流体风和磁约束喷流的数值研究。 临界现象的工作目标是理解与其他领域（如统计物理学）中临界现象的联系，探索崩溃临界行为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学上不同的例子。 关于合并黑洞双星的工作的目标是在两个空间维度（2+1）中开发和探索黑洞的视视界内边界条件的使用，并开发有效利用并行架构的算法。 在这两种情况下，2+1中开发的知识都将扩展到三个维度（3+1）。 关于食星的工作将侧重于研究非线性等离子体不稳定性的简单分析/数值模型，这可能与短周期、低质量系统有关，并研究相对论脉冲星风和正常恒星风之间的相互作用。 将继续开发在上一个资助期开始的通用磁流体动力学代码（AVATAR），并将其应用于磁流体动力学风的自准直和磁约束射流传播的研究。

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.