引引力波偏振  

The polarizations of gravitational waves

作　　者：郜青 龚云贵 梁迪聪 Qing Gao;Yungui Gong;Dicong Liang(School of Physical Science and Technology, Southwest University, Chongqing 400715, China;School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China)

机构地区：[1]西南大学物理科学与技术学院,重庆400715 [2]华中科技大学物理学院,武汉430074

出　　处：《科学通报》2018年第9期801-815,共15页Chinese Science Bulletin

基　　金：国家自然科学基金(11690021;11605061);中央高校基本科研业务费(XDJK2017C059;SWU116053)资助

摘　　要：引力波的直接观测不但开启了一扇探测引力本质的全新窗口,而且使我们进入了多信使引力波天文学时代.引力波不影响单个检验粒子的测地线运动,其偏振态由两个相邻检验粒子的相对运动,即测地线偏离运动所决定.测地线偏离方程中只出现黎曼张量的电分量,它有6个独立分量,所以在最一般的度规引力理论中,引力波最多可以有6种偏振模式.这6种偏振模式分别为:"+"偏振态、"×"偏振态、呼吸偏振态、矢量-x偏振态、矢量-y偏振态及纵振态.爱因斯坦广义相对论中的引力波只有"+"与"×"两个张量偏振态,Brans-Dicke理论中的引力波除了"+"与"×"偏振态外,还有一个呼吸偏振态.在Horndeski及f(R)理论中,引力波除了"+"与"×"两个张量偏振态外,还有一个由呼吸模与纵振模混合而成的标量偏振态.在爱因斯坦-以太理论中,非零矢量场的出现破坏了局域洛伦兹对称性,该理论中的引力波以非光速传播,且具有5个独立偏振态.张量-矢量-标量理论中的引力波传播速度与光速不同,且该理论中的引力波具有6个独立偏振态.因为不同引力理论中的引力波偏振态不同,所以引力波偏振态的测量可用于探究引力本质.The direct detection of gravitational waves opens a new window to probe the nature of gravity,and it brings us into the era of multi-messenger astronomy.Gravitational wave has no effect on the geodesics of a test particle,but it affects the relative motion between two nearby test particles.To measure gravitational wave and its polarizations,we need to study the geodesic deviation equation for two nearby test particles.Since only the electric part of the Riemann tensor Ri0 j0 appears in the geodesic deviation equation and it has six independent components,there are up to six possible polarization states in general metric theories of gravity.In terms of the electric part of the Riemann tensor,the six polarizations are defined mode,andthe longitudinal mode.For weak,plane and null gravitational waves,these six polarizations can be classified based on their properties under the Lorentz transformation.In Einstein’s general relativity,the gravitational waves are tensor waves and there are＂＋＂and＂×＂modes of polarization.In Brans-Dicke theory,in addition to the＂＋＂and＂×＂polarization states,the scalar breathing mode also appears,and all these three polarizations are transverse modes.In the most general scalar-tensor theory of gravity,the Horndeski theory,the massive scalar field excites both the breathing and the longitudinal modes,so in addition to the＂＋＂and＂×＂polarizations,there exists a single mix state consisting of both the breathing and the longitudinal modes.In the massless limit,the longitudinal mode disappears and the mix state becomes the pure transverse breathing polarization as that in Brans-Dicke theory.The nonlinear f（R）theory of gravity can be written as a scalar-tensor theory of gravity,so the polarization states in f（R）gravity are the same as those in Horndeski theory except that there is no massless limit in f（R）gravity.In Einstein-Aether theory,due to the existence of the unit timelike vector field,the local Lorentz invariance is violated.The gravitational wav

关 键 词：引力波偏振态 标量-张量理论 爱因斯坦-以太理论 张量-矢量-标量理论 

分 类 号：O412.1[理学—理论物理]