标题： 量化准正则模态系统的激发 显示英文标题

标题： Quantifying excitations of quasinormal mode systems

摘要： 由黑洞过程产生的强场引力波的计算产生了以准正常（QN） ringing 为主波形，这是一种黑洞特有的阻尼振荡。 我们在这里描述了量化所产生的波形中的QN内容的数学问题。 这是通过几个步骤完成的：(i) 我们发展了QN系统的数学理论，这些系统是完整的（在将要定义的意义上），并表明存在一个量，“激发系数”，似乎具有量化QN内容所需的特性。 (ii) 我们表明不完整的系统可以（至少有时）转换为物理等效的完整系统。 最显著的是，我们给出了一个特定修改模型问题的完整性严格证明。 (iii) 我们评估了模型问题的激发系数，并证明激发系数的实用性有限。 最后，我们讨论了QN激发量化的普遍问题，并提出了一些关于正常模态和QN系统之间不可避免差异的推测。 显示英文摘要

摘要： Computations of the strong field generation of gravitational waves by black hole processes produce waveforms that are dominated by quasinormal (QN) ringing, a damped oscillation characteristic of the black hole. We describe here the mathematical problem of quantifying the QN content of the waveforms generated. This is done in several steps: (i) We develop the mathematics of QN systems that are complete (in a sense to be defined) and show that there is a quantity, the ``excitation coefficient,'' that appears to have the properties needed to quantify QN content. (ii) We show that incomplete systems can (at least sometimes) be converted to physically equivalent complete systems. Most notably, we give a rigorous proof of completeness for a specific modified model problem. (iii) We evaluate the excitation coefficient for the model problem, and demonstrate that the excitation coefficient is of limited utility. We finish by discussing the general question of quantification of QN excitations, and offer a few speculations about unavoidable differences between normal mode and QN systems.