Gravitational Radiation from Black Holes

波，如水，声音和电磁波，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测是，加速物体会产生引力波，类似于电荷产生电磁波的方式。目前，引力波只能通过消耗同轨恒星的能量来间接探测。已经建造了一个激光干涉重力波观测站（LIGO），预计它将通过直接探测这些波开辟一种新的天文学形式。引力波最强大的来源是两个共轨黑洞的螺旋和合并。计算机模拟为LIGO提供了必要的理论细节，以调整引力信号并监测合并的动力学。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不够。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引力波，该方法使用与计算数学家合作开发的求解爱因斯坦方程的技术，并在测试问题上进行彻底校准，并作为爱因斯坦工具包中的社区资源实施。这些技术将进一步发展，以测量引力波携带的能量和角动量的损失，以及双黑洞螺旋的其他物理特性，如电磁辐射对应物。该方法利用基于辐射传播的光锥的特征演化。大多数计算工作是基于时间演化使用柯西初值问题。邦迪和彭罗斯对光锥的广义相对论的初值问题进行了重新表述，这使得人们首次对引力辐射有了清晰的认识。这里提出的全局策略结合了柯西演化的内部区域包含的黑洞与外部区域中的特征演化沿沿着光锥延伸到无限远。特征演化导致了第一个三维代码，它可以成功地定位，跟踪，演化和计算单个扭曲，旋转和移动黑洞的波形。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，目前的柯西码需要有限的人工外边界，这在提取波形时引入了低效率和错误。建议的工作集成了互补的优势，柯西和特征进化提供了一个准确的全球治疗。

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.