Gravitational Radiation from Black Holes

该奖项支持对爱因斯坦广义相对论革命性预测的研究，即加速物体产生引力波，类似于电荷产生电磁波的方式。波，如水、声波、弹性波和电磁波，是物理系统的一个显著特征。该项目以前的工作涉及应用数学、计算、引力理论和天体物理学的国际专家，并导致了新的方法，这些方法已被应用于广泛的一类问题，如地震学。在导致诺贝尔奖的历史性科学事件中，引力波最近被激光干涉引力波天文台(LIGO)探测到。这一初步探测有力地证实了爱因斯坦的理论。在与欧洲处女座引力波天文台的合作下，它开启了一种新的天文学形式，将扩大我们对宇宙的知识。最初探测到的强大引力波是两个共轨道黑洞激发和合并的结果。这一戏剧性的事件所产生的兴奋导致了公开演讲的大量听众，并激励了年轻人才进入该领域。尽管爱因斯坦的方程式描述了引力波的产生，但其复杂性和非线性使纯粹的分析方法变得不够用。这就需要将计算方法引入广义相对论。该项目的一个主要目标是开发新的方法来计算双黑洞激励的引力波形和其他物理性质，如能量动量损失和角动量损失。该方法利用基于辐射在其上传播的光锥的特征进化。大多数计算工作是基于使用柯西初值问题的时间演化。邦迪和彭罗斯用光锥重新表述了广义相对论的初值问题，这导致了对引力辐射的第一次清晰的理解。特征演化导致了第一个代码，它可以成功地定位、跟踪、演化和计算单个扭曲、旋转和运动的黑洞的波形。然而，在二元问题中，光锥的聚焦导致内部焦散，这阻止了纯粹的特征方法。另一方面，目前的柯西编码需要有限的人工外边界，这在提取波形时引入了模糊性和误差。这里所追求的全球战略结合了包含黑洞的内部区域的柯西演化和沿着光锥延伸到无穷远的外部区域的特征演化。这整合了柯西和特征演化的互补优势，并导致了特征波提取工具，作为爱因斯坦工具包的一部分，可供数值相对论社区使用。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports studies of the revolutionary prediction of Einstein's general theory of relativity that accelerated bodies produce gravitational waves, analogous to the way electric charges produce electromagnetic waves. Waves, such as water, sound, elastic and electromagnetic waves, are a prominent feature of physical systems. Previous work on this project involved international experts spanning applied mathematics, computation, gravitational theory and astrophysics and led to new methods which have found application to a broad class of problems, e.g. seismology. In a historic scientific event leading to a Nobel prize award, gravitational waves were recently detected by a Laser Interferometric Gravity Wave Observatory (LIGO). This initial detection was a resounding confirmation of Einstein's theory. In collaboration with the European Virgo gravitational wave observatory, it opens a new form of astronomy which will expand our knowledge of the universe. The powerful gravitational waves in the initial detection resulted from the inspiral and merger of two co-orbiting black holes. The excitement generated by this dramatic event has led to overflow audiences at public lectures and has inspired young talent to enter the field.Although Einstein's equations describe the production of gravitational waves, their complexity and nonlinearity make a purely analytic approach inadequate. This necessitated the introduction of computational methods into general relativity. A main goal of the project is to develop new methods for computing the gravitational waveform and other physical properties of binary black hole inspirals, such as the energy-momentum and angular momentum loss. The approach utilizes characteristic evolution based upon the light cones on which the radiation propagates. Most computational work is based upon time evolution using the Cauchy initial value problem. The reformulation of the initial value problem for general relativity in terms of light cones by Bondi and by Penrose resulted in the first clear understanding of gravitational radiation. Characteristic evolution has led to the first code which could successfully locate, track, evolve and compute the waveform for a single distorted, spinning and moving black hole. However, the focusing of the light cones in a binary problem leads to interior caustics which prevent a purely characteristic approach. On the other hand, present Cauchy codes require a finite artificial outer boundary which introduces ambiguity and error in extracting the waveform. The global strategy pursued here combines Cauchy evolution in the interior region containing the black holes with characteristic evolution in the exterior region extending along the light cones to infinity. This integrates the complementary strengths of Cauchy and characteristic evolution and has led to a characteristic wave extraction tool which is available to the numerical relativity community as part of the Einstein Toolkit.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.