## The Superluminal Phenomenon of Light For The Kerr-Newman Black Hole

**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. The black hole have the rotation term a and the charge term RQ with the Schwarzschild radius RS. The geodesic of light 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 occurrence of the superluminal phenomenon for r between RS and (R_Q^2+a^2 sin^2 θ/2)/R_S at sinθ>0 when RQ∼RS. The calculations of the velocity of light reveal that the maximum speed of light and the range of the superluminal phenomenon are much related to the rotational term a. 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 reference frame and the black hole is not heavy, these results of the superluminal phenomenon are suitable for the observations by an observer in a reference frame at infinity or very weak gravitation like on Earth.

**Comments:** 16 Pages.

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### Submission history

[v1] 2018-08-07 08:08:13

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