【作者】 王璇；

【导师】 贺观圣；

【作者基本信息】 南华大学 ， 数学， 2025， 硕士

【摘要】 运动引力系统时变场中检验粒子传播及有关相对论效应的全面解析探讨对相对论天体物理学和基本天体测量学具有重要意义。本文对光线及相对论性中性有质量粒子在平动黑洞引力场中的动力学及其传播过程中的弱场引力偏折效应展开了详细的理论研究。众所周知,作为广义相对论最早的、最经典的预言之一的引力偏折(或引力透镜)效应在现代天体物理学中具有广泛的应用。为便于研究运动黑洞时变场中检验粒子传播规律及其引力偏折现象,本文基于爱因斯坦场方程(一种二阶非线性偏微分方程)的广义协变性,采用洛伦兹推动技术首次在Kerr-Schild坐标系中获得了场方程关于任意常速运动的克尔-纽曼黑洞的精确解。基于该运动黑洞度规的弱场形式,我们在二阶后闵可夫斯基(PM)近似框架内探讨了沿极轴方向以常速运动的克尔-纽曼黑洞极轴面内光线的弱场引力偏折效应。本文首先获得了该运动黑洞极轴面内光线的动力学方程的解析式。然后,我们结合适当的边界条件和初始条件,采用迭代技术求解了该动力学方程,从而获得了极向运动的克尔-纽曼黑洞极轴内光线的2PM引力偏折角的解析式。最后,我们还讨论了该透镜的极向运动对其极轴面内光信号的引力偏折产生的影响,并估计了探测这种运动学效应的可能性。此外,我们也探讨了沿径向平动的克尔-纽曼黑洞赤道平面内光信号的弱场偏折效应。作为上述精确度规在弱场极限下的另一典型应用,本文探讨了以二维速度在赤道面内运动的史瓦西黑洞引起的相对论性粒子(含相对论性有质量粒子和光子)的首阶引力偏折效应。我们获得了一个有关该时空中相对论性粒子首阶引力偏折角的统一公式。当透镜的横向速度分量为零时,该公式与文献中给出的径向平动史瓦西源引起的相对论性粒子的弱场偏折结果吻合得很好。另外,我们还在广义相对论框架下统一讨论了该黑洞的横向和径向运动对相对论性有质量粒子和光子的一阶史瓦西偏折的影响,并分析了这种联合的运动学效应的量级及其天文探测的可能性。本文所获得的运动克尔-纽曼黑洞的严格度规及对作用于检验粒子弱场引力偏折的透镜运动效应的探讨有望为未来的天文观测提供有意义的理论支撑。更多还原

【Abstract】 A full analytical probe of propagation of test particles and related relativistic effects in time-dependent fields of a moving gravitational system are of great importance in modern relativistic astrophysics and fundamental astrometry.This paper perform a detailed theoretical study on the dynamics of light rays and relativistic neutral massive particles,along with the gravitational deflection effects during their propagation in the weak-field limit,in the gravitational field of a moving black hole with a translational velocity.As is well known,gravitational deflection effects(or gravitational lensing),acting as one of the earliest and most classical predictions of general relativity,has widespread applications in modern astrophysics.To facilitate the study of the propagation laws and the gravitational deflection phenomena of test particles in the time-dependent field of a moving black hole,we base on the general covariance of Einstein’s field equations(a set of second-order nonlinear partial differential equations),and adopt the Lorentz boosting technique to obtain an exact solution of the field equations with respect to a moving Kerr-Newman black hole with an arbitrary constant velocity in the Kerr-Schild coordinate system for the first time.Based on the weak-field form of the metric of the moving black hole,we probe the weak-field gravitational deflection effect of light in the polar-axis plane of a moving Kerr-Newman black hole with its constant velocity along the polar axis,within the framework of the second-order post-Minkowski(PM)approximation.This paper first obtains the analytical form of the dynamical equations of the light traveling in the polar-axis plane of the moving black hole.By combining with proper boundary and initial conditions,we then use an iterative technique to solve the dynamical equations,and thus obtain the analytical expression of the 2PM gravitational deflection angle of light propagating in the polar-axis plane of a moving Kerr-Newman black hole whose velocity is along its polar axis.Finally,we also discuss the influence of the poloidal motion of the lens on the polar-axis-plane gravitational deflection of light signals,and estimate the possibility of detecting this kinematical effect.Additionally,we also investigate the weak-field equatorial deflection effect of light signals in the spacetime of a moving Kerr-Newman black hole whose velocity is in a radial direction.As another typical application of the mentioned exact metric in the weak-field limit,this paper investigates the gravitational bending effects of relativistic particles(including both relativistic massive particles and photons)up to the leading order caused by a moving Schwarzschild black hole with a two-dimensional equatorial velocity.We obtain a unified formula for the gravitational bending angles of relativistic particles up to the leading order in this spacetime.When the transverse component of the lens velocity vanishes,this formula agrees well with the previous results of the weak-field deflection of relativistic particles induced by a radially moving Schwarzschild source.In addition,within the framework of general relativity,we discuss the influences of the transversal and radial motions of the black hole on the Schwarzschild bending up to the first order of relativistic massive particles and photons,and analyze the magnitude of this joint kinematical effect and the possibility of its astronomical detection.It is expected that the exact metric of a moving Kerr-Newman black hole obtained in this paper,along with the probe of the lens motion effects the on the weak-field gravitational deflection of test particles,could provide meaningful theoretical support for future astronomical observations.更多还原