中文摘要：

综述广义相对论中引力波的研究,主要报告有关残余引力波和引力辐射方面的系列研究结果.先简介引力波方程和基本物理概念,然后讨论含有扰动二阶项的非线性场方程,引力波的能动张量,短波平均,残余引力波的压强定义和高频发散扣除等问题.给出膨胀宇宙中残余引力波的解析解,覆盖了从极早期暴涨到现阶段加速膨胀的各阶段,给出任何时刻和波长都成立的功率谱、能量密度和压强谱,讨详细论了暴涨阶段原初谱的定义,简介现阶段谱的各频段可能探测,主要讨论目前运行的激光干涉探测器对谱的限制和信噪比,给出残余引力波所诱导的微波背景辐射的磁场型偏振的解析谱.最后基于后牛顿近似,计算OJ287双黑洞的轨道、引力辐射能流、波形等,讨论了双星的质心漂移问题.

英文摘要：

We report the results of our systematic studies of gravitational wave in general relativity,including relic gravitational wave（RGW） and gravitational radiation of binary. First we introduce the gravitational wave field equation and physical concepts involved,and discuss the nonlinear field equation containing second order terms of perturbations,the energy-momentum tensor of gravitational wave,its short-wavelength average,the definition of pressure,and removal of high-frequency divergences,etc. We present the exact solution of RGW,which covers the whole cosmic expansion history,from inflation to the present accelerating stages. We give the power spectrum,the spectral energy density and pressure,which are valid at any time and wavenumber,discuss the issue of the primordial spectrum defined during inflation,and give a brief review of current detections at various wave-bands,focus mainly on laser interferometers,give the signal-noise ratios and constraints upon RGW. We also present the analytical spectrum of magnetic polarization induced by RGW. Finally,we present the results of our study of OJ287 as a binary black holes,and give the the orbit,the energy flux,and waveform,and also discuss the shifting of the center-of-mass.