Gravitational Radiation from Black Holes

波，如水、声波和电磁波，是物理系统的一个突出特征。爱因斯坦广义相对论的一个革命性预言是，加速的物体会产生引力波，类似于电荷产生电磁波的方式。目前，引力波只能通过消耗共轨脉冲星能量的方式间接探测到。激光干涉引力波天文台（LIGO）已经建成，预计将通过直接探测引力波开辟一种新的天文学形式。最强大的引力波来源是两个共轨黑洞的激励和合并。计算机模拟为LIGO调节引力信号和监测合并动态提供了必要的理论细节。爱因斯坦的方程描述了引力波的产生，但它们的复杂性使得纯粹的分析方法是不够的。这就需要在广义相对论中引入计算方法。该项目的目标是开发先进的方法来模拟黑洞产生的引力波。该方法使用了与计算数学家合作开发的解决爱因斯坦方程的技术，对测试问题进行了彻底校准，并作为爱因斯坦工具包中的社区资源实现。该技术将进一步发展，以测量引力波带走的能量和角动量的损失，以及双黑洞灵感的其他物理特性，如电磁辐射对应。该方法利用基于辐射传播的光锥的特征演化。大多数计算工作都是基于柯西初值问题的时间演化。邦迪和彭罗斯用光锥重新表述广义相对论的初值问题，使人们第一次清楚地认识了引力辐射。本文提出的全局策略将包含黑洞的内部区域的柯西演化与沿光锥延伸至无限远的外部区域的特征演化相结合。特征演化导致了第一个能够成功定位、跟踪、演化和计算单个扭曲、旋转和运动黑洞波形的三维代码。然而，在二元问题中，光锥的聚焦会导致内部焦散，从而阻止了纯特征方法。另一方面，目前的柯西码需要一个有限的人工外边界，这在提取波形时带来了低效率和错误。提出的工作整合了柯西和特征演化的互补优势，以提供准确的全局处理。

Waves, such as water, sound and electromagnetic waves, are a prominent feature of physical systems. A revolutionary prediction of Einstein's general theory of relativity is that accelerated bodies produce gravitational waves, analogous to the way electric charges produce electromagnetic waves. At present, gravitational waves have only been detected indirectly by the way they deplete energy from co-orbiting pulsars. A Laser Interferometric Gravity Wave Observatory (LIGO) has been constructed that is expected to open up a new form of astronomy by direct detection of these waves. The most powerful source of gravitational waves is the inspiral and merger of two co-orbiting black holes. Computer simulations provide the theoretical details necessary for LIGO to tune in the gravitational signal and monitor the dynamics of the merger. Einstein's equations describe the production of gravitational waves but their complexity makes a purely analytic approach inadequate. This has necessitated the introduction of computational methods into general relativity. The project's goal is to develop advanced methods to simulate the production of gravitational waves from black holes.The approach uses techniques for solving Einstein's equations which have been developed in collaboration with computational mathematicians, thoroughly calibrated on test problems and implemented as a community resource in the Einstein toolkit. The techniques will be further developed to measure the loss of energy and angular momentum carried off by gravitational waves, and other physical properties of binary black hole inspirals, such as the electromagnetic radiation counterpart. 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. The global strategy proposed 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. Characteristic evolution led to the first 3-dimensional code which could successfully locate, track, evolve and compute the waveform for a single distorted, spinning and moving black hole. However, in a binary problem, the focusing of the light cones 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 inefficiency and errors in extracting the waveform. The proposed work integrates the complementary strengths of Cauchy and characteristic evolution to provide an accurate global treatment.