利用多频段引力波天文学检验修改引力理论

在观察到由大质量双恒星级黑洞体系发射的引力波之后，人们很快意识到可以利用空间和地面探测器在不同波段上探测同源发射的引力波。尽管多频段引力波天文学自2016才兴起，但是它将对物理学和天文学产生深远的影响。特别是，它将提供一个独特的检验强引力场中的修改引力理论的新方法。在此项目中，我们将完成以下四个方面的工作：（1）把广义相对论中的后牛顿近似方法推广到修改引力理论的N体问题中，并考虑二阶近似的贡献；（2）在这些修改引力理论中计算两体体系在旋进（inspiral）阶段的各种物理量，如引力波形、极化、能量和角动量损失率等，并研究由自旋为0和自旋为1的引力子激发的单极子和偶极子效应；（3）系统地研究大质量恒星级黑洞系统，并识别可由空间探测器（如LISA、天琴和太极）和地面探测器（如LIGO、Virgo和KAGRA）探测到的引力波信号；（4）利用多频段引力波天文学甄别修改引力理论。

With the observations of gravitational waves from very massive binary stellar black holes, it becomes possible to detect gravitational waves emitted from the same source by both space-borne and ground-based detectors. In particular, the gravitational wave first detected in the human history by LIGO in 2015, would have been visible to space-borne detectors in the mHz band, such as LISA, TianQin or TiaJi, for several years prior to its detection in the 100 Hz band by LIGO. This multi-band gravitational wave astronomy just emerged in 2016 and has profound implications to physics and astronomy. In particular, it will provide a unique tool to test modified theories of gravity in the strong gravitational field regime. In this proposal, using the post-Newtonian approximations, we shall systematically study the emission and propagation of gravitational waves in the inspiral phase of massive binary compact objects right before their coalescence in modified theories of gravity, and pay particular attention to Einstein-aether theory. This is a theory that is self-consistent and satisfies all the observational constraints carried out so far. Its Cauchy problem is well-posed and yet violates the Lorentz symmetry, a corner stone of modern physics. More specifically, we shall carry out our investigation by following the four different steps: (1) Generalize the post-Newtonian approximations developed in general relativity for the N-body problem to modified theories of gravity up to the second order post-Newtonian approximations. (2) Accurately calculate observational variables of binary systems in their inspiral phase in such theories, including their gravitational waveforms, polarizations, energy and angular momentum loss rates, and study the monopole and dipole effects, due the presence of spin-0 and spin-1 gravitons often appearing in these theories. (3) Systematically investigate the massive stellar binary black hole systems, and identify gravitational wave signals that are detectable by the space-borne detectors, such as LISA, TianQin and TiaJi, and ground-based ones, such as LIGO, Virgo and KAGRA. (4) Test modified theories of gravity using the multi-band gravitational wave astronomy.