The Superluminal Phenomenon of Light Near the Kerr–Newman Black Hole or Super-Gravitational Source - Pei, Ting-Hang (Frontiers in Physics, 2021)
We use the Kerr-Newman metric based on the general relativity to discuss the observed superluminal phenomenon of light near the black hole whether it is observable astronomically at infinity or the weakly gravitational place like on the Earth. The black hole has the rotation term a and the charge term RQ as well as the Schwarzschild radius RS. The geodesic of light in the spacetime structure is ds2=0 and the equation for three velocity components (dr/dt, rdθ/dt, rsinθdϕ/dt) is obtained in the spherical coordinate (r, θ, ϕ) with the coordinate time t. Then three cases of the velocity of light (dr/dt, 0, 0), (0, rdθ/dt, 0), and (0, 0, rsinθdϕ/dt) are discussed in this research. According to our discussions, only the case of (dr/dt, 0, 0) gives the possibility of the observations of the superluminal phenomenon at r between RS and (R_Q^2+a^2 sin^2 θ/2)/R_S at sinθ>0 when RQ~RS. The results reveal that the maximum speed of light and the range of the superluminal phenomenon are much related to the rotational term a and the charged term RQ. It is at least reasonable at two poles and in the equatorial plane when light propagates along the radial direction. Generally speaking, the superluminal phenomena for light can possibly occur in these cases that the radial velocity dr/dt is dominant and the other two velocity components are comparably small. When the relative velocity between the observer coordinate frame and the black hole is not large, the superluminal phenomenon is possibly observable at infinity or in a weakly gravitational frame like on the Earth. The results can also be applied on the super-gravitational sources.