Research On Plane-fronted Gravitational Wave

Since Einstein proposed the general relativity and predicted the existence of gravitational waves,nearly a century has passed.With the prediction,doubt and belief about the existence of gravitational waves,until the laser interference gravitational wave observatory(LIGO)detected the first gravitational wave event,GW150914,we finally confirmed the existence of gravitational waves,but our understanding of gravitational waves is still very scant.Limited by the current detection technology and accuracy,it’s necessary to study gravitational waves theoretically.At the same time,theoretical research on gravitational waves may also affect the development direction of detection technology to a certain extent.The purpose of this thesis is to explore the exact solution of gravitational waves,discussing the polarization states of gravitational waves to test gravitational theories,calculating the energy momentum pseudotensor of gravitational field to obtain the relationship between them and the metric.Firstly,this thesis introduces the linear approximate solutions obtained under the weak field approximation in general relativity,and then discusses three exact solutions of Einstein’s field equations,which are Bondi solution,Peres solution and Liu-Chou solution.All these three solutions are plane gravitational wave solutions.After that,some properties of plane gravitational waves are mainly introduced,they are the polarization information of gravitational waves and the energy and momentum information carried by themselves.Then we introduced a method of analyzing the polarizations of gravitational waves—the Newman-Penrose method and E(2)group classification.For the energy and momentum information of the gravitational field,several different energy and momentum pseudotensor expressions are introduced,which were defined by Einstein,Bergman,Tolman,and Landau,Lifschitz.Then this thesis used the Newman-Penrose method to analyze the polarization states of the three exact solutions.Both the Bondi solution and the Peres solution contain the "+" polarization.While the Liu-Chou solution have the "+" and "×" modes.This is the same as weak field result.Then,according to different energy and momentum pseudotensor expressions,the energy and momentum information of the gravitational field for the three gravitational wave solutions are calculated.It is found that different expressions have the same results for the same plane gravitational wave solution.In addition,the results of these four energy-momentum pseudotensor expressions for the Peres solution are always zero.Finally,this thesis briefly introduces two modified gravitational theories,which are Brans-Dicke theory and f(R)theory.We also introduce their linear vacuum solutions.At the same time,we briefly discussed the modified theory of BD theory BDV and BDΛtheory.This thesis also used the Newman-Penrose method to analyze the polarization of gravitational waves in the Brans-Dicke theory,and finds that it has one breathing polarization mode more than those in general relativity.Because the polarization state of the modified gravity theory is different from that of the general relativity,the general relativity can be tested based on the measurements of polarization state of gravitational wave.