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 theory of general relativity to discuss the observed superluminal phenomenon of light near the black hole and whether it is observable astronomically at infinity or a weak gravitational place such as on 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 Boyer-Lindquist coordinates (r, θ, and ϕ) with the coordinate time t. Then, three cases of the velocity of light (dr/dt, 0, and 0), (0, rdθ/dt, and 0), and (0, 0, and rsinθdϕ/dt) are discussed in this research. According to our discussion, only the case of (dr/dt, 0, and 0) gives the possibility of the observations of the superluminal phenomenon and an example is shown at r between RS and (RQ2+a2sin2θ/2)/RS 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. Although the superluminal phenomenon is discussed in the Boyer-Lindquist coordinates, all the results are easy to be transformed or discussed in the Cartesian coordinates (x, y, z, t) by setting R2 = x2+y2+z2 = r2+a2sin2θ and rdr = RdR in the velocity of light. The conclusions of the superluminal phenomenon about the three velocity components (dR/dt, Rdθ/dt, Rsinθdϕ/dt) are different from them in the Boyer-Lindquist coordinates. Generally speaking, the superluminal phenomena for light can possibly occur in these cases where 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 weak gravitational frame such as on Earth. The results can also be applied on the super-gravitational sources.