Study On The Light Bending And Gravitational Lensing In Brans-Dicke Theory

The early Newtonian gravitational theory predicted that the light ray passed through the vicinity of gravitational field around the compact celestial body would occur bending phenomenon.Then Einstein made the same prediction in relativity theory because of the bending nature of the time-space around the compact celestial body,and worked out the planet precession angle and the light deflection angle in the spherical symmetry weak field approximation.The deflection phenomenon of light ray in the gravitational field is called the gravitational lensing effect,and the compact celestial body deflecting the light ray is regarded as the gravitational lens.In modern astronomy,the gravitational lensing phenomena is usually used to study the related properties of the gravitational field and the distribution of its mass.Therefore,it is regarded as an important tool for detecting dark matter and energy.As two important candidates of gravitational theory,the relativity theory and Brans-Dicke gravitational are used to explain celestial body,formation and evolution of the universe have key role.In this paper,we will investigate the planet precession,light bending and gravitational lensing effect in relativity theory and Brans-Dicke gravitational theory framework.In chapter one,we introduce the basic definitions and properties of the planet preces-sion,light bending and gravitational lensing effect in gravitational theories,and then the domestic and international development in this issue.Then we point out the innovation and significance of of our works in the end of this chapter.In chapter two,we derive the general orbital equation for a free particle moving in the static,spherically symmetric spacetime by a spherical star.Then,we write down the corresponding equations,which are nonlinear ordinary differential equations,of motion for the planet and light ray by using the spherically symmetric solutions to these vac-uum field equations in these two theories.Finally,the approximation solutions to the equations of motion can be obtained by perturbation method,which will yield the angles corresponding to the planet precession and light deflection.In chapter three,the general integral expression of the light bending angle,in the static,spherically symmetry spacetime,is derived by eliminating the time coordinate of particle geodesic equation in the isotropic coordinate system.In the weak field limit,the metric in the integral expression is expanded a Taylor series with a parameterized post-Newton method(PPN),which can be used to obtain the light bending angle accurate to the fourth-order correction;Based on the the study of light bending,the gravitational lensing equation is used to calculate the positions of the lens images accurate to third order in the perturbation parameter ?=V_·/V_E,and further working out magnifications of the lens images,total magnification and centroid accurate to third order.For the Brans-Dicke gravitational theory,starting from the static,spherically symmetric solu-tion of Brans-Dicke field equation in isotropic coordinate system,we finally give the corresponding high-order corrections of the bending angle,lensed image positions and magnifications,total magnifications and weighted-centroid position.In chapter four,we summarize and discuss these results of the planet precession,light bending and gravitational lensing effect in gravitational theory,also propose some prospects for future related research.These results presented in this paper will help us to check and distinguish these two theories of gravity using high-precision experimental observation.