Binary Black Holes and Gravitational Radiation

在过去的五年中，描述黑洞及其运动一直是数值相对论激烈活动背后的主要推动力。从这一探索中开发了大量的工具，特别是那些由双黑洞合作产生的工具。然而，尽管计算机技术、数值算法和对爱因斯坦场方程的理解取得了进步，但对最后几个轨道和黑洞双星系统合并的模拟仍未实现。宾夕法尼亚州立大学小组的主要目标将是继续发展，并整合成一个完整的解决方案，碰撞和辐射问题，这个黑洞碰撞之谜的缺失部分，与匹兹堡，德克萨斯和波茨坦的小组密切合作。宾夕法尼亚州立大学的工作将主要集中在两个密切相关的领域：i)视界边界条件和ii)适用于包含移动黑洞的时空3+1演化的规范或坐标条件。移动的黑洞，3+1演化到目前为止已经完成了利用等距条件，对于正面碰撞的情况，或分析失效和位移条件，对于增强的单个黑洞系统。消除运动黑洞奇点的完全视界边界条件尚未完全实现。同样，到目前为止，很少有研究完全解决了为控制场变量的非物理增长（也称为网格拉伸）的三维演化构建规范条件的问题。为了研究黑洞演化的这两个基本方面，我们将考虑以下三个问题：1)被提振的单个黑洞；2)黑洞的散射；3)双星系统的单轨和并合。这些问题建立在复杂性之上（移动单一视界、引力辐射、多重视界、旋转网格等）；因此，他们提供了一个自然的一步一步的路径来挑选和解决黑洞演化的具体方面，直接关系到通用的灵感黑洞合并的最终目标。这些问题的成功解决方案将代表着超越计算前沿的进步。黑洞的散射和双星系统轨道或合并的模拟将产生关于引力辐射和相互作用奇点性质的有价值的信息。此外，这一努力的相关性延伸到与黑洞碰撞模拟相关的基本含义之外；同样重要的是，之前的研究和合作模式的连续性，以及双黑洞联盟开发的基础设施的使用。特别是合作将发挥关键作用，因为目前的工作不会直接考虑外部边界条件、初始数据和并行化等重要领域的工作

***9800970LagunaDescribing black holes and their motion has been the main thrust behind the intense activity in Numerical Relativity during the last half decade. A large number of tools have been developed from this quest, in particular those arising from the Binary Black Holes collaboration. However, in spite of the advancements in computer technology, numerical algorithms and understanding of Einstein's field equations, simulations of the last few orbits and the coalescence of black hole binary systems have not yet been achieved. The primary objective of the group at Penn State will be to continue developing, and integrating into a complete solution to the collision and radiation problem, the missing components of this Black Hole Collision Puzzle, in close collaboration with the groups at Pittsburgh, Texas and Potsdam. The effort at Penn State will mainly focus on two closely related areas: i) apparent horizon boundary conditions and ii) gauge or coordinate conditions applied to 3+1 evolutions of spacetimes containing moving black holes. Moving black hole, 3+1 evolutions have so far been performed taking advantage of isometry conditions, for the case of head-on collisions, or analytic lapse and shift conditions, for boosted single black holes systems. A complete apparent horizon boundary condition to excise moving black hole singularities has not yet been fully implemented. Similarly, up to this point, few studies have completely addressed the issue of constructing gauge conditions for 3D evolutions which control unbound unphysical growth of field variables, also known as grid stretching. To investigate these two fundamental aspects of black hole evolutions, the following three problems will be considered: i) boosted single black holes, ii) scattering of black holes and iii) single orbit and merger of binary systems. These problems build upon complexity (moving single apparent horizon, gravitational radiation, multiple apparent horizons, corotating meshes, etc.); thus, they provide a natural step-by-step path to single out and solve specific aspects of black hole evolutions, directly relevant to the ultimate goal of generic inspiral black hole coalescences.Successful solutions to these problems will represent progress beyond that exclusively in the computational front. Scattering of black holes and simulations of an orbit or coalescence of binary systems will yield valuable information regarding gravitational radiation and the nature of interacting singularities. Furthermore, the relevance of this effort extends to more than its fundamental implications in connection with black hole collision simulations; equally important will be the continuity of previous studies and collaborative models, as well as the use of infrastructure developed by the Binary Black Holes Alliance. Collaborations, in particular, will play a crucial role since work on important areas such as outer boundary conditions, initial data and parallelization will not be directly considered by the present effort.***