Research in Gravitation Theory and Relativistic Astrophysics

该奖项支持广义相对论以及数学天体物理学中的相关问题的研究，其中强引力场发挥着有趣的作用。这项研究的总体范围包括引力天体物理学中的问题，其中分析数学、应用数学和计算数学的见解可用于帮助解释高级 LIGO 的引力波探测。特别是，这里支持的项目将提高我们对中子星碰撞的理解，提供对此类物体核成分的见解。他们还将研究在不同几何特征的时空中求解控制黑洞和中子星动力学的爱因斯坦方程的影响。这些研究项目可分为三个特定领域：中子星物理、引力波数据分析和数值相对论。这些研究将允许对中子星的观测和我们对强引力场的理解被用来确定中子星状态方程，而无需对中子星物质的微观物理做出任何假设。 他们还将帮助引力波模拟界确定其波形模型的准确性，这些模型在检测和解释天体物理引力波信号方面发挥着重要作用。这里描述的数值相对论研究涉及开发求解具有任意空间拓扑的流形上的爱因斯坦方程的技术。 这些方法将用于研究各种问题，包括努力探索流体系统中湍流级联的引力模拟，并以数值方式探索宇宙学模型，以确定是否以及如何通过观测来识别非平凡拓扑。

This award supports research in general relativity theory, and related problems in mathematical astrophysics, in which strong gravitational fields play an interesting role. The general scope of this research includes problems in gravitational astrophysics in which insights from analytical, applied, and computational mathematics can be used to help interpret gravitational waves detections by Advanced LIGO. In particular, the projects supported here will improve our understanding of neutron star collisions, providing insights into the nuclear composition of such objects. They will also study the impact of solving the Einstein equations, which govern the dynamics of black holes and neutron stars, in spacetimes of different geometrical characteristics. The research projects can be grouped in three specific areas: neutron star physics, gravitational-wave data analysis, and numerical relativity. These studies will allow observations of neutron stars and our understanding of strong gravitational fields to be used to determine the neutron-star equation of state in a way that is free from any assumptions about the microphysics of neutron star matter. They will also help the gravitational wave simulation community determine the accuracy of their waveform models that play an essential role in detecting and interpreting astrophysical gravitational wave signals. The studies in numerical relativity described here involve developing techniques for solving Einstein's equations on manifolds with arbitrary spatial topologies. These methods will be used to study a variety of problems, including an effort to explore the gravitational analog of the turbulent cascade seen in fluid systems, and exploring cosmological models numerically to determine whether and how non-trivial topology could be recognized through observations.