| Gravitational waves (GW's) can be detected based on their tidal effect. The first way of detecting GW's is mass resonance method, in which the typical one is Weber bar. With the invention of high-quality interferential laser, the optical methods based on mass resonance principle were considered, e.g. LIGO (Laser Interferometer Gravitational-wave Observatory), LISA (Laser Interferometer Space Antenna) and VIRGO (VIRGO is the collaboration between Italian and French research teams, for the realization of an interferometric gravitational wave detector). However, their working frequency band is only ~10~{-7}-10~4Hz, and the precision predicted by LISA and VIRGO is 10~{-22}-10~{-23}/Hz, traditional mass resonance GW's detecting methods are not applicable to GW's which frequency are greater or much greater than 10~4Hz.High-frequency GW's (HFGW) (10~4-10~{13}Hz, especially high-frequency GW's in microwave frequency band) can be detected by the electromagnetic (EM) methods. According to General Relativity, the propagation velocity of GW's equals light speed, i.e. c, thus there is a good interferential effect between GW's and EM waves. The perfect situation for EM detection of GW's is resonance of GW's to EM waves. The practical meaning is as follows: general astronomical GW's resource, strong EM resonant system, high-energy particle beam, high-temperature plasma, and crystal array can generate HFGW which frequency reaches 10~8Hz or higher. Such HFGW can not be detected by traditional detecting equipments. Maximal signal and peak of high-frequency relic GW's, recently predicted by quintessential inflationary models (QIM), may be firmly localized in the gigahertz region, which is just the best frequency band of HFGW for EM response. Recent development of relative technology such as superconducting resonant cavity with high quality factor, squeezed quantum states, quantum non-demolition measurements, ultra strong laser physics and high energy laboratory astrophysics, etc., provide the technological possibilities for the EM detection of HFGW.In this paper, the important physical quantities, e.g. energy density, energy flux density, momentum density and momentum flux density are analyzed based on GR and electrodynamical equations in curved spacetime. The results in curved space-time are compared with them in flat space-time. Some new issue and foundation are shown for EM response to GW's and other relative astronomical observation.The developments of GR theories are introduced first, and then the HFGW resources, the history of the interaction between HFGW and EM fields are reviewed.The EM energy-momentum tensor in spherical symmetric static gravitational fields, both polarized weak gravitational plane wave, and high-frequency standing GW's in cylindraceous EM resonant cavity are discussed in detail. By comparing with the responding results of flat space-time, the gravitational influence to electromagnetic energy-momentum tensor is researched. By numerical calculation, the results are quantificationally studied, and the numerical results have important meaning for further theoretical research and practical observation about electromagnetic response of GW's.The major researched achievements in this paper are as follows:(1) The EM energy-momentum tensors outside spherical symmetric charged mass, spherical symmetric mass immerged in uniform magnetic field and spherical symmetric mass with magnetic moment are discussed. The results are useful to show ulterior character of some celestial bodies (e.g. neutron stars, and black-hole etc.), and provide some new possible observational effects for the relative astronomical observation.(2) The perturbative effect of Gaussian beam to both polarized weak plane gravitational wave perturbation of passing through a static magnetic field is discussed, and the first- and second-order perturbative EM energy-momentum tensor and their numerical result are gotten. The results show that the net increment of electromagnetic perturbative energy of whole system is extremely smal...
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