Simulating angular momentum of gravitational field of a rotating black hole and spin momentum of gravitational waves

Abstract

In this research, we simulated the angular momentum of gravitational field of a rotating black hole and the spin momentum of gravitational waves emitted from the black hole. At first, we calculated energy densities of the rotating gravitational field and spinning gravitational waves as the vectors, which were projected on the spherical curved surface of the gravitational field and of the gravitational waves. Then we calculated the angular momentum and the spin momentum as the vectors perpendicular to the curved surface. The earlier research by Paul Dirac, published in 1964, did not select the curved surface to calculate the motion of quantum particles; but, instead, he chose the flat surface to develop the theory of quantum mechanics. However, we pursued the simulation of the gravitational waves in spherical polar coordinates that form the spherical curved surface of the gravitational waves. As a result, we found that a set of anti-symmetric vectors described the vectors that were perpendicular to the spherical curved surface, and with these vectors we simulated the angular momentum of the rotating black hole’s gravitational field and the spin momentum of gravitational waves. The obtained results describe the characteristics of the rotation of a black hole and of spinning gravitational waves.

Simulation of a rotating strong gravity that reverses time

“…In this research we used the same curvature tensors that we derived and used in our previous researches [1][2][3]:…”

“…We used the same assumption of our previus researches [1][2][3] for simulating the distortion of time and space, as shown in Fig. 1, 2.…”

“…We use the same algorithm that we used for our previous research [1][2][3] to simulate the relative strengths (intensities) of the curvature tensors, which are reflected by the stress-energy tensor that is placed at the end of the distance r in Fig. 1, 2.…”

“…In our previous research [1] we simulated a rotating strong gravity, in which time and space are distorted; and we found that the direction of the angular momentum changes as the strong gravity changes its frequency of the rotation. However, the scope of the previous research was limited to the space components.…”

“…In the previous research [1] we assumed that the component of the rotation matrix of the spherical polar coordinates of  has anti-symmetric components,  sin 22 R…”