修正引力在铃宕过程中引力扰动和辐射研究

Owing to LIGO's detections of the gravitational waves (GWs) from binary black hole mergers, the studies of GWs have attracted lots of attention recently, and the properties of GWs have been investigated from various aspects. It is expected that the next generation detectors of GWs will observe the details of GWs emitted during the ringdown phase of a binary system of two compact stars and furthermore, the experimental observations would have a significant impact on the theories of gravitation and the fundamental physics. In the present project, we propose to study the properties of the emissions of GWs during the ringdown phase and obtain the quasi-normal mode spectra of black holes in various modified theories of gravity. We shall focus on the identifications of the differences among the modified theories of gravity and general relativity, and place these theories directly under the tests of GW observations. In modified theories of gravity without Lorentz symmetry, particles can travel with speeds larger than that of light, and then the Killing horizons are no longer the boundaries of black holes. As a result, the quasi-normal mode frequencies in such theories are intrinsically different from those given in general relativity, which can serve as a key observational evidence for theories with broken Lorentz invariance.

随着LIGO宣布探测到双黑洞合并产生的引力波，人们对引力波的性质产生了极大的兴趣。研究者估计下一代的引力波探测器可以对双致密星合并的铃宕（Ringdown）阶段的细节进行观测，其观测结果将对引力理论及其涉及到的物理基础原理产生重大影响。因此本项目将研究各种修正引力中的铃宕阶段的性质，得到各种引力中的黑洞似正规模频谱。并根据此频谱找出修正引力与广义相对论的不同，做出可与实验比对的科学预言。对于洛仑兹对称性破缺的修正引力而言，我们还必须考虑黑洞视界在Killing视界以内的情况，因此这时得到的黑洞似正规模与广义相对论的结果有区别，这可以作为洛仑兹破缺与否的关键判据。

该项目研究修正引力理论中的黑洞铃宕(Ringdown)阶段引力辐射特征。通过对黑洞似正规模的计算，可以在理论上确定铃宕阶段的引力波波形。因此我们研究了各种修正引力中的铃宕阶段的性质，得到了各种引力中的黑洞似正规模特征，并根据这些特征对比修正引力与广义相对论的不同，做出可与实验对比的科学预言。在这三年的研究中，我们找到了若干修正引力中的黑洞背景时空解及其似正规模振动特征，研究了动态黑洞的似正规模，改进了矩阵法，圆满完成了项目的研究计划。