Study Of Relativistic Effects In Gravitational Field Of A Moving Black Hole

This dissertation applies the Lorentz boosting method to obtain two exact and two weak-field solutions of field equations in harmonic coordinates,including exact metrics for constantly moving Schwarzschild and Reissner-Nordstr?m black holes,and second post-Minkowskian order metrics for constantly moving Kerr and Kerr-Newman black holes,respectively.Based on the background metrics,the post-Newtonian(or weak-field)dynamics of test particles are respectively derived.A new iterative technique in the post-Minkowskian approximation is further proposed to study the three observable relativistic effects caused by a radially moving Kerr-Newman black hole in detail,containing the second-order gravitational deflections of light and relativistic massive particles,and the second-order gravitational time delay as well as gravitational shift of frequency of light.The velocity effects induced by the motion of the black hole on these relativistic effects are also discussed.More concrete results are listed as follows.We first derive solutions of Einstein's field equations for moving black holes.On the basis of general covariation of field equations,we apply a Lorentz transformation to the Schwarzschild metric in harmonic coordinates and obtain the exact metric of a uniformly moving Schwarzschild black hole.As an application,we calculate the dynamics of test particles propagating in the weak field of the moving central body.A Lorentz boosting is also used to get the exact metric of a moving Reissner-Nordstr?m black hole with an arbitrary constant velocity and thus the post-Newtonian equation of motion of a massive particle.Moreover,the weak-field metrics up to the second post-Minkowskian order for moving Kerr and Kerr-Newman black holes with an arbitrary constant velocity are obtained respectively by the same method,with the post-Newtonian dynamics of test particles given.Up to the first post-Minkowskian order,the consistency between our metric via Lorentz boosting and the retarded Liénard-Wiechert potential solution of field equations is proved.Starting from the weak-field metric of a moving Kerr-Newman black hole with a constant radial velocity,we then derive the equations of motion of relativistic test particles propagating in the equatorial plane of the lens,which are solved by the post-Minkowskian iterative technique and numerical integration method,respectively.A general formulation for the second-order gravitational deflection angle of both photons and relativistic massive particles due to the moving lens is achieved.Accordingly,the analytical form for the second-order Schwarzschild deflection angle of relativistic massive particles in the previous work is confirmed.We also discuss the velocity effects induced by the motion of the lens on the second-order contributions to the gravitational deflection from both numerical and analytical points of view,and consider the possibilities of their detection via high-accuracy telescopes.The analytical forms for the second-order gravitational time delay of light signals induced respectively by a stationary Kerr-Newman source and the radially moving Kerr-Newman source are also obtained.For the former lens,our result verifies the existence of the largest second-order Schwarzschild contribution to the gravitational time delay.For the latter,our result in the first post-Minkowskian approximation matches well with that based on the Liénard-Wiechert representation.The velocity effects on the gravitational time delay are discussed in detail,and their magnitudes and the possibilities of their detection are analyzed.We find that it's possible to detect the correctional effects on the second-order Schwarzschild and Kerr contributions to the time delay via nowadays high-accuracy astronomical techniques.Finally,we derive the second-order gravitational frequency shift of light caused by the moving Kerr-Newman source analytically and investigate the velocity effects on it.We find that the radial velocity effect on the first-order frequency shift is as significant as the transversal velocity effect and thus cannot be neglected,when the light emitter or the receiver is close to the gravitational lens with the distance between them being an impact parameter scale.The significant velocity effect is usually transient.