RUI: Studies in Numerical Relativity

爱因斯坦的广义相对论描述了宇宙中所有的引力相互作用，从把一个掉落的苹果拉向地球的力，到宇宙本身的膨胀。广义相对论的方程——被称为爱因斯坦方程——相当复杂，只有在非常特殊和不现实的情况下，才能用铅笔和纸精确地解出来。模拟更现实的场景——例如，为了理解两个合并黑洞发出的引力波信号，并由LIGO引力波天文台探测到——需要计算机模拟。该小组正在进行的研究工作旨在开发这种计算机模拟的方法和途径。近年来，PI开发了新的方法，这些方法非常适合于一类新的问题，并且可能使当前的模拟显着提高效率。在接下来的几年里，他计划采用这些方法来研究发生在黑洞形成初期的所谓“临界现象”，检查快速旋转的中子星的特性，并与同事合作，使上述新方法在公共社区代码中可用。本科生将参与这些活动，为他们提供“动手”的研究经验，并在鲍登学院创造一个丰富的研究学习环境。本研究在数值相对论方面的科学目标包括发展和实现求解爱因斯坦广义相对论方程的数值算法，以及它们在相对论性物体，特别是中子星和黑洞的数值模拟中的应用。在下一个资助期内，PI计划采用先前在NSF资助下开发的球面极坐标数值相对论方法来研究引力物理和相对论天体物理学中的几个问题，特别是使用该代码来研究缺乏球面对称的临界坍缩。扩展先前的结果，PI计划研究角动量和非球面变形对完美流体、标量场和真空时空中引力坍缩的关键现象的影响，解决几个悬而未决的问题。PI还计划对天体物理物体进行模拟；具体来说，就是新型差速旋转中子星的稳定性。最后，PI将在有效和可扩展的社区代码（即Einstein Toolkit和Harm3D）中实现这些曲线坐标下的数值相对论方法，以便这些技术可以应用于当前独立代码无法执行的许多天体物理模拟。

Einstein's theory of general relativity describes all gravitational interactions in the universe, ranging from the force that pulls a falling apple to the Earth, to the expansion of the Universe itself. The equations of general relativity - called Einstein's equations - are quite complicated and can be solved exactly, i.e. with pencil and paper, only under very special and unrealistic circumstances. Modeling more realistic scenarios - for example in order to understand a gravitational wave signal, emitted by two merging black holes, and detected by the LIGO gravitational wave observatory - requires computer simulations. This group's ongoing research efforts aim at developing methods and approaches for such computer simulations. In recent years, the PI has developed new methods that are well suited for a new class of problems, and that may make current simulations significantly more efficient. In the next few years he plans to adopt these methods to study so-called "critical phenomena" that occur at the onset of back-hole formation, to examine properties of rapidly rotating neutron stars, and to collaborate with colleagues to make the above-mentioned new methods available in public community codes. Undergraduate students will participate in these activities, providing them with a "hands-on" research experience, and generating a research-enriched learning environment at Bowdoin College.The scientific goals of this research effort in numerical relativity include the development and implementation of numerical algorithms for the solution of Einstein's equations of general relativity, as well as their application in the numerical modeling of relativistic objects, in particular neutron stars and black holes. In the next funding period the PI plans to adopt methods for numerical relativity in spherical polar coordinates, previously developed with support from NSF grants, to study several problems in gravitational physics and relativistic astrophysics, in particular, to use this code to study critical collapse in the absence of spherical symmetry. Extending earlier results the PI plans to study the effects of angular momentum and aspherical deformations on critical phenomena in the gravitational collapse of perfect fluids, scalar fields, and vacuum spacetimes, addressing several open questions. The PI also plans to perform simulations of astrophysical objects; specifically, the stability of new types of differentially rotating neutron stars. Finally, the PI will implement these methods for numerical relativity in curvilinear coordinates in efficient and scalable community codes, namely the Einstein Toolkit and Harm3D, so that these techniques can be applied in a number of astrophysical simulations that cannot be performed with current stand-alone codes.