The Energy-Momentum Tensor Of Relic Gravitational Waves And Electromagnetic Fields In The Weak Plane Gravitational Waves

Gravitational waves (GWs) can be detected based on their tidal effect. The first method of detecting GWs 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^-4-10⁴Hz, and the sensitivity predicted by LISA and VIRGO is 10^-22-10^-23/Hz. So the traditional mass resonance GWs detecting methods are not applicable to GWs whose frequency are greater or much greater than 10⁴Hz . High-frequency GWs (HFGW) (～10⁴-10¹³Hz, especially high-frequency GWs in microwave frequency band) can be detected by the electromagnetic (EM) methods. According to General Relativity, the propagation velocity of GWs equals light speed, i.e. c, there is a good interferential effect between GWs and EM waves. The resonance of GWs to EM waves is the most ideal method.In this paper, the development of GR theories is introduced first, then the HFGW resources and the history of the interaction between HFGW and EM fields are reviewed. The main part of this paper is to calculate the energy-momentum tensor of relic gravitational waves in the de Sitter spacetime and discuss the perturbative effect of Gaussian beam to the double polarized weak plane gravitational waves through a static magnetic field.The major research achievements in this paper are as follows:(1) Using Einstein-Tolman's expression of energy-momentum pseudo-tensor, we calculate the energy-momentum tensor of relic gravitational waves in the de Sitter spacetime. The positive definite property of the energy density and the rationality of the momentum density are discussed. In particular, we calculate the energy density of GWs produced by the inflationary stage in detail and also discuss the positive definite property of it. The relic gravitational waves produced by the inflationary stage carried plenty of original information of the initial universe. If we can detect it, the birth and the evolvement of the universe will be more clearly known.(2) The perturbative effect of Gaussian beam to the weak plane gravitational waves through a static magnetic field is discussed, and the first- and second-order perturbative EM energy-momentum tensor and their numerical results are gotten. The results show that the net increment of electromagnetic perturbative energy of the system is extremely small, but the physical behavior of EM fields (i.e. the spread direction, polarized states, distribution and phase etc.) would change in local region of EM system. The results are useful to display extreme weak GWs signal.