We will mainly discuss the measurable angle (local angle) of the light ray ψP at the position of the observer P instead of the total deflection angle (global angle) α in Kerr spacetime. We will investigate not only the effect of the gravito-magnetic field or frame dragging due to the spin of the central object but also the contribution of the motion of the observer with a coordinate radial velocity vr = dr/dt and a coordinate transverse velocity bvϕ = bdϕ/dt, where b ≡ L/E is the impact parameter (L and E are the angular momentum and the energy of the light ray, respectively) and vϕ = dϕ/dt is a coordinate angular velocity. vr and bvϕ are computed from the components of the four-velocity of the observer ur and uϕ, respectively. Because the motion of observer causes an aberration, we will employ the general relativistic aberration equation to obtain the measurable angle ψP which is determined by the four-momentum of the light ray kμ and the four-momentum of the radial null geodesic wμ as well as the four-velocity of the observer uμ. The measurable angle ψP given in this paper can be applied not only to the case of the observer located in an asymptotically flat region but also to the case of the observer placed within the curved and finite-distance region. Moreover, when the observer is in radial motion, the total deflection angle αradial can be expressed by αradial = (1 + vr)α static; this is consistent with the overall scaling factor 1 − v instead of 1 − 2v with respect to the total deflection angle αstatic in the static case (v is the velocity of the lens object). On the other hand, when the observer is in transverse motion, the total deflection angle is given by the form αtransverse = (1 + bvϕ/2)α static if we define the transverse velocity as having the form bvϕ.

中文翻译：

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克尔时空中的广义相对论像差方程和光线可测角

我们将主要讨论光线的可测量角度（局部角度）ψ磷在观察者的位置磷而不是总偏角（全局角度）α在克尔时空中。我们将不仅研究重力磁场或由于中心物体自旋引起的框架拖动的影响，而且还将研究观察者运动与坐标径向速度的贡献vr = dr/d吨和坐标横向速度bvφ = bdφ/d吨,在哪里b ≡ 大号/乙是影响参数（大号和乙分别是光线的角动量和能量）和vφ = dφ/d吨是坐标角速度。vr和bvφ由观察者四速度的分量计算得出你r和你φ， 分别。由于观察者的运动会引起像差，我们将使用广义相对论像差方程来获得可测量的角度ψ磷由光线的四动量决定ķμ和径向零测地线的四动量wμ以及观察者的四速你μ. 可测量角度ψ磷本文给出的不仅可以应用于位于渐近平坦区域的观察者的情况，也可以应用于位于弯曲和有限距离区域内的观察者的情况。此外，当观察者在径向运动时，总偏转角α径向可以表示为α径向 = (1 + vr)α 静止的; 这与整体比例因子一致1 - v代替1 - 2v相对于总偏角α静止的在静态情况下（v是镜头物体的速度）。另一方面，当观察者处于横向运动时，总偏转角由以下形式给出α横 = (1 + bvφ/2)α 静止的如果我们将横向速度定义为具有形式bvφ.