Authors: Ting-Hang Pei
We use the Kerr-Newman metric based on the general relativity to discuss the superluminal phenomenon of light at the black hole whether it is observable astronomically at infinity or the weakly gravitational place like on Earth. The black hole have 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, r*sinθ*dϕ/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, r*sinθ*dϕ/dt) are discussed in this research. According to our discussions, only the case of (dr/dt, 0, 0) gives the possibility of the occurrence of the superluminal phenomenon for r between RS and (R_Q^2+a^2*(sinθ)/^2 2)/R_S at sinθ>0 when RS~RQ. 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 Earth.
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