Resonances of quasinormal modes and orbital motion in general relativistic compact binaries

致密天体的准正则模包含了许多关于这类天体内部结构的信息，在这个意义上就像一个指纹。因此，对于未来的引力波天文学来说，准正则模的测量可能是一个有趣的问题。这将为了解中子星的内部结构提供重要途径。在这个研究项目中，将考虑激励性双星中准正则模和轨道运动之间的共振。这是一个特例，在天体物理上非常现实的情况下，准正常模式是如何被激发的。由黑洞和/或中子星组成的吸气式致密双星预计将被未来的引力波天文学定期观测到。一个重要的问题是，下一代引力波探测器的测量必须有多精确，才能在这种特殊情况下对中子星的准正常模式做出声明。这项研究项目将通过推导出一个分析框架来描述上述广义相对论共振，从而为回答这个问题提供基础。过去已经考虑过准正常模和轨道运动之间的共振以及它们对引力波形的影响。然而，最近有人指出，包含广义相对论效应可以实质上改变结果。这个研究项目的重要方面是，它旨在对这种共振进行明显的协变(尽管在某些方面只是近似的)分析描述，从而为这种效应提供一个一般的相对论框架。此外，我想在被称为规范-重力二元性的研究领域获得经验，因为这是从事引力理论工作的物理学家进行跨学科研究的最丰富的领域之一。准正规模式也在那里找到了应用。

Quasinormal modes of compact astrophysical objects contain much information about the internal structure of such objects and are in this sense like a fingerprint. Therefore a measurement of quasinormal modes could be an interesting problem for future gravitational wave astronomy. This would provide an important way to learn something about the internal structure of, e.g., neutron stars. In this research project resonances between quasinormal modes and orbital motion in an inspiralling binary shall be considered. This is a special case how quasinormal modes can be excited in an astrophysically very realistic situation. Inspiralling compact binaries consisting of black holes and/or neutron stars are expected to be observed by future gravitational wave astronomy on a regular basis. An important question is how accurate the measurements of upcoming generation of gravitational wave detectors must be to make statements about quasinormal modes of neutron stars in this special case. This research project shall provide the foundation to answer this question by deriving an analytic framework to describe the mentioned resonance in general relativity.Resonances between quasinormal modes and orbital motion as well as their impact on gravitational waveforms have been considered already in the past. However, it was pointed out recently that including general relativistic effects can substantially change the result. The important aspect of this research project is that it aims at a manifestly covariant (though in some respect only approximate) analytic description of such resonances, thus providing a general relativistic framework for this effect.Further I would like to gain experience with the field of research known as gauge-gravity duality, as this is one of the most fertile areas for physicists working on gravitational theory to conduct interdisciplinary research. Quasinormal modes also find applications there.