The Superluminal Phenomenon of Light Near the Kerr-Newman Black Hole or Super-Gravitational Source

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 R-Q as well as the Schwarzschild radius R-S. The geodesic of light in the spacetime structure is ds(2) = 0, and the equation for three velocity components (dr/dt, rd theta /dt, rsin theta d phi /dt) is obtained in the Boyer-Lindquist coordinates (r, theta, and phi) with the coordinate time t. Then, three cases of the velocity of light (dr/dt, 0, and 0), (0, rd theta /dt, and 0), and (0, 0, and rsin theta d phi /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 R-S and (RQ2 + a2 sin 2 theta/2) / RS at sin theta >0, when R-Q similar to R-S. 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 R-Q . 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 R-2 = x(2)+y(2)+z(2) = r(2)+a(2)sin(2)theta and rdr = RdR in the velocity of light. The conclusions of the superluminal phenomenon about the three velocity components (dR/dt, Rd theta/dt, Rsin theta d phi/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.

Automated summary

In this study, the Kerr-Newman metric based on the theory of general relativity is used to discuss the potential of observing superluminal phenomenon of light near a black hole. The results show that the rotational term a and the charge term R-Q are closely related to the maximum speed of light and the range of the superluminal phenomenon. The study highlights that the superluminal phenomenon for light may be observable in cases where the radial velocity component is dominant, with the other two components being comparatively small.