Numeric Simulation of Artificial Antigravity upon General Theory of Relativity

Abstract

which reported the result of the numeric simulation on the artificial antigravity. This paper further describes the derivation of the idea of the artificial antigravity, and adds the simulation of angular momentum that is needed to describe the antigravity. Also, because the angular momentum is the perpendicular movement to a threedimensional curved surface in a four-dimensional space-time, this paper challenges the limit of applying the curvature tensor in quantum mechanics; while, current quantum mechanics has been established on the flat surface. The artificial rotation of a hypothetical object is simulated, in which the gravity is so strong that the time-space can be distorted. The spherical polar coordinate system is selected to describe the curvature of the space, and the curvature tensor is formulated. Then the tensor is multiplied by the Euler's rotation matrix to make the inner product for the gravitational energy and the outer cross-product for the angular momentum of the rotation. To simulate the distorted time-space, two cases are selected: the linear distortion and the non-linear distortion upon the distance from the center of the strong gravity; also, the speed of the rotation is set in two options: the slower and the faster. Then the equation of motion is set by the curvature tensor to calculate the coefficient of the gravitational energy on the surface of the sphere in the spherical polar coordinates, and to calculate the coefficient of the angular momentum in the perpendicular direction to the sphere. The result shows that the antigravity can be produced by rotating the object, and the angular momentum can show the opposite directions by the selection of the rotation speed.

Numeric Simulation on the Waves from Artificial Anti-gravity upon General Theory of Relativity

“…The vectors of the matrix X should hold the projected image of the energy intensity on the surface of the sphere in the spherical polar coordinates. (Note: The surface of the sphere refers to Figure 14 of [2] (p. 52).…”

“…The spin angular momentum is to be projected on the flat surface, which is perpendicular to the curved spherical surface in the spherical polar coordinate system. (Note: The flat surface refers to Figure 15 of [2] (p. 53).…”

“…Figure 2 and Figure 3 show the input data that simulate the distortion of time and space, which we used also for the previous research [1,2]. In these figures, r is the distance from the center of the strong gravity; t is the time to travel for the distance; τ is the distorted time by the equation (31), which expands and shrinks depending on r and t; and, ρ is the distorted distance by the equation (32), which expands and shrinks depending on t and r. For the distorted time and space, two models are set: Case-1 (non-linear model) and Case-2 (linear model) as shown in Table 1, which assign the functions of f(r) of the equation (31) and g(r)…”

“…This research is an extended version of the work presented at the 2020 IEEE 2 nd International Conference on System Analysis_Intelligent Computing (SAIC) held in Kyiv, Ukraine, in October 2020 [1] as well as the consequently published paper [2] from the Advances in Science, Technology and Engineering Systems Journal in May 2021. These papers reported that a rotating object would produce anti-gravity, if it held a heavy mass that would distort time and space.…”

“…These papers reported that a rotating object would produce anti-gravity, if it held a heavy mass that would distort time and space. The last paper [2] informed of the waves emitted from the rotating object; however, the report of the analysis was forwarded to this new paper because the numeric simulation required a separate research.…”