General relativistic aberration equation and measurable angle of light ray in Kerr spacetime

We will mainly discuss the measurable angle (local angle) of light ray $\psi_P$ at position observer $P$ instead total deflection (global $\alpha$ in Kerr spacetime. investigate not only effect gravito-magnetic field or frame dragging but also contribution motion with a coordinate radial velocity $v^r$ and transverse $bv^{\phi}$ ($b$ is impact parameter $v^{\phi}$ angular velocity) which are converted from components 4-velocity $u^r$ $u^{\phi}$, respectively. Because causes an aberration, we employ general relativistic aberration equation to obtain $\psi$. The $\psi$ given this paper can be applied case located asymptotically flat region placed within curved finite-distance region. Moreover, when motion, $\alpha_{\rm radial}$ expressed by radial} = (1 + v^r)\alpha_{\rm static}$ consistent overall scaling factor $1 - v$ respect $\alpha{\rm static case. 2v$ where $v$ lens object. On other hand, form transverse} bv^{\phi}/2)\alpha_{\rm if define as having $bv^{\phi}$.