The Energy-Momentum Tensor Of Gravitational Waves Of The Double Polarized States And Electromagnetic Fields In Gravitational Waves

The existence of gravitational waves (GW's) is one of the most important consequences of General Relativity(GR),it is the dimple of curved space-time in essence. Nowadays, the problem of GW's has become one of the focus which both theoretical and experiment physics pay a lot attention to. The developments in gravitational theory has been reviewed.the theory of gravitational radiation and technique of GW's detection have been introduced,especially electromagnetic response of high-frequency gravitational waves(HFGW).As main task of this thesis,the problem of GW's energy-momentum and the perturbation to electromagnetic field by HFGW in the resonant cavity have been discussed.According to Landau-Lifshitz prescription of energy-momentum tensor of gravitation field,the concrete forms of energy-momentum densities of cylindrical gravitational waves of the double polarized states have been calculated in Cartesian coordinates system. Positive definition property of energy density and symmetrical property of the momentum density components have been analyzed. Furthermore, the concrete forms of energy-momentum densities of plane gravitational waves of the double polarized states have been calculated,the positive definite property of the energy density have been analyzed .The positive definition property of the GW's energy density and rationality of the GW's momentum density have been proved, and therefore the asymptotic behavior of high-frequency gravitational waves (HFGW) is easy to explain. Moreover, according to GR, the speed of gravitational waves is equal to that of light, thus there is a good interferential effect between GW's and EM waves. The perfect situation is the resonance of GW's to EM waves. In a particular EM resonant cavity, the static magnetic filed and wave of the background EM make up a GW's resonance system. The action of GW's on the static magnetic field produces perturbative EM fields and the resonance occurs between the perturbative EM fields and background EM waves. In this paper, we have calculated energy-momentum tensors of first order and second order perturbations that GW's take action with background EM waves. By numerical calculation, the results are quantificationally studied.The technique of GW's exploration is a very complicated system engineering,and also has a very important reference value to the further theoretical research about electromagnetic response of GW's and experiment technique of GW's exploration.