Test Of A Model Coupling Of Electromagnetic And Gravitational Fields By Using High-frequency Gravitational Waves

Observations in recent years have found that the current universe is accelerating it-s expansion.In order to give a reasonable explanation for this phenomenon,physicists have revised and expanded the standard Einstein theory of gravity.The introduction of space-time curvature to couple with the material field is one of the important ways for this research.This type of coupling model is often called the non-minimum coupling model between the material field and the space-time curvature.In particular,people have conducted extensive and in-depth research on the coupling model of electromagnetic field and gravitational field.In order to fully understand the interaction between electromagnet-ic fields and gravitational fields,various ideas about how photons couple with curved space-time have been proposed Successively.Among these models,studying the coupling of photons and Weyl tensors is one of the feasible methods.Weyl tensor can describe the gravitational curvature of space-time.Through the propagation of light signals in gravita-tional fields,the coupling of photons and Weyl tensors provides us with an opportunity to examine the interaction between electromagnetic fields and gravitational fields.In this paper we use the coupling model of Maxwell's electromagnetic field and the Weyl tensor of the gravitational field to study how the wave vector of the electromagnetic wave is affected by the plane gravitational wave in the coupling model.By introducing the orthogonal frame and the antisymmetric combination of the frame,we express the Weyl tensor in the background of plane gravitational wave space-time as a more concise form.Then,in order to solve the motion equation of photons in the coupled model more conveniently,the linear combination of momentum components is introduced,and the e-quation of motion is expressed in matrix form.By calculation,the difference between the two wave vectors k^?and(?)^?is proportional to??²?h₊or??(|?|h₊)^1/2,which indicates that the coupling effect of electromagnetic field and the gravitational field is weak for low-frequency waves,but becomes significant for high-frequency waves.The difference be-tween the two wave vectors depends on the polarization,electromagnetic wave frequency?,gravitational wave frequency?,coupling parameter?and the angle?between the lightpropagation direction and the coordinate axis.We observe that for the case of??(|?|h₊)^1/2,the value of?satisfy the observability condition in all three different gravitational wave frequency ranges.However for the case of??²?h₊,the observability condition for?is not satisfied for low frequency gravitational waves,although it is satisfied for high frequency gravitational waves.The results indicate that we can use the detection of high frequency gravitational waves to test the model coupling of the Maxwell field to the Weyl tensor of the gravitational field.