Study Of Post-Newtonian Motion And Gravitational Wave Radiation In Binary Star Systems

The motion of an object in a gravitational field and its gravitational wave radiation are classical problems in astronomy and physics,and are central to the theory of general relativity.The three classical predictions of general relativity,"perihelion motion of Mercury,light deflection,and gravitational redshift",are in good agreement with experiments.The discovery of pulsating binary systems by Taylor and Hulls in 1974 and the measurement of the orbital period of these systems are in good agreement with the theoretical prediction of the change in the period of gravitational systems with the loss of energy from gravitational wave radiation,thus indirectly proving the existence of gravitational waves.The classical prediction of "gravitational waves" was further confirmed by the general theory of relativity.This thesis focuses on the proposed Keplerian motion of binary star systems and their gravitational wave radiation laws,as follows.In the first part,we study the analytical solution of the proposed Keplerian motion of the non-spin binary system under the second-order post-Newtonian(2PN)approximation.First,the dynamical equations of the binary system in the second-order post-Newtonian approximation are given directly.Second,the analytical solution of the binary motion in the second-order post-Newtonian approximation based on the Wagoner-WillEpstein-Haugan representation is derived by applying the post-Newtonian iteration method.Again,the parameters of the proposed Keplerian motion in the second-order post-Newtonian approximation are derived,as well as the relations between the orbital period and orbital incoming motion with the orbital energy and angular momentum.Finally,the Keplerian equations of the binary motion and the relations between the parameters are derived when the extreme mass ratio tends to zero.The derived conclusions can be used to calculate the gravitational wave radiation and provide an important basis for constructing a theoretical template for gravitational waves.In the second part,we derive the loss rate of the gravitational radiation of the system under the post-Newtonian approximation.First,the secondorder post-Newtonian gravitational wave radiation-induced system energy loss rate of spinless binary systems that has been obtained is derived based on the gravitational wave radiation formula for binary systems under the post-Newtonian approximation developed by Epstein and Wagoner.Second,the study of the system momentum and angular momentum loss rates due to second-order post-Newtonian gravitational wave radiation is carried out.In the era of gravitational wave astronomy,the study of the second-order post-Newtonian gravitational wave radiation-induced reactions becomes timely and necessary.The research in this thesis is of great scientific significance and practical application because it can help people to better understand the motion of objects and their gravitational wave radiation patterns,and can provide theoretical references for space gravitational wave detection.