RUI: WoU-MMA: 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。对更一般的场景进行建模需要计算机模拟。该奖项支持的持续研究工作旨在开发此类计算机模拟的方法和途径，并利用这些模拟来探索相对论天体物理学和广义相对论的过程。在接下来的几年里，这将包括与广义相对论的本质有关的未解决的问题——任意小的黑洞能否形成？——以及辐射对新形成的中子星和黑洞吸积的影响。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。这些研究工作的科学目标包括开发和实现求解爱因斯坦广义相对论方程的数值算法，以及将其应用于相对论性物体的数值建模，特别是中子星和黑洞。在下一个筹资期内，这些活动将集中于两个主要领域的项目，即黑洞引力坍缩的关键现象和辐射的动态影响。对于前者，重点将放在临界解不可能是球对称的情况上。在以往关于临界坍缩的研究经验和见解的基础上，这些现象将被用于探索真空时空中引力波的坍缩，这是一个重要的问题，即使在它第一次被解决25年后，人们仍然知之甚少。关于后者，将实施辐射转移的近似处理，并用于探索辐射可能发挥重要动力学作用的几种情况。例子包括超大质量恒星的演化直到径向不稳定的开始，可能由原始中子星冷却引发的非轴对称不稳定，以及对黑洞吸积中的超级爱丁顿流的探索。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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 general scenarios requires computer simulations. Ongoing research efforts supported by this award aim at developing methods and approaches for such computer simulations, and to use these simulations to explore processes in relativistic astrophysics and general relativity. In the next few years this will include unresolved questions pertaining to the nature of general relativity — can arbitrarily small black holes form? — as well as effects of radiation in newly formed neutron stars and on black-hole accretion. 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 these research efforts 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 these activities will focus on projects in two main areas, namely critical phenomena in the gravitational collapse to black holes, and dynamical effects of radiation. With regard to the former, the focus will be on situations in which the critical solution cannot be spherically symmetric. Building on experience and insights from previous work on critical collapse, these phenomena will be explored for the collapse of gravitational waves in vacuum spacetimes, an important problem that remains poorly understood even 25 years after it was first tackled. With regard to the latter, an approximate treatment of radiation transfer will be implemented and used to explore several scenarios in which radiation may play an important dynamical role. Examples include the evolution of supermassive stars up to the onset of radial instability, possible non-axisymmetric instabilities triggered by cooling in proto-neutron stars, and an exploration of super-Eddington flows in accretion onto black holes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.