Study On Parameterized Post-post-newtonian Light Propagation In The Field Of One Spherically-symmetric Body

The motion of photon in gravitational field is an important research content of general relativity.Light deflection,time delay and gravitational redshift are classical predictions of general relativity,which agree well with the observed values under the post-first-order Newtonian approximation.With the development of science and technology and the continuous improvement of observation level,the high-order post-Newtonian effect of gravitational field on light propagation will be observed.The parameterized Newtonian(or post-Newtonian)framework can represent the weak field metric of many kinds of gravity theories including general relativity,so it is often used as the background of gravitational field to study the motion laws of objects including photons.The work of this paper mainly includes the following three parts:In the first part,based on the universal second-order post-Newtonian parameterized spherically symmetric metric,the affine contact method and Lagrange equation method are used to derive the kinetic equation and the null-geodesic equation of the experimental particles including photons respectively.In the second part,the propagation trajectories of light rays under the second order post Newtonian approximation are derived by iterative method.First,we give the accelerations,velocities and trajectories of photons in the post-zero order Newtonian approximation(Minkowski space-time).Secondly,the correction terms of photon velocity and trajectory under the first order Newtonian approximation are derived.The motion of the photon is decomposed into two directions parallel to and perpendicular to the initial velocity direction.For parallel directions,the first-order correction term of velocity can be obtained directly from optical subclass optical geodesics.For the vertical direction,the first order correction term of photon velocity in this direction is obtained by integrating the first order post-Newtonian dynamics equation of photon.The first order correction term of velocity is integrated,and then the correction term of trajectory is obtained.Thirdly,the correction terms of photon velocity and trajectory under the post-second order Newtonian approximation are derived.The derivation method is similar to the correction term of photon velocity and trajectory in Newton's approximation after derivation of first order.In the third part,the deflection Angle and time delay of the light in the gravitational field are calculated by using the velocity and trajectory of the photon under the second-order post-Newtonian approximation.