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Yoshinari Minami*
Advanced Science-Technology Research Organization, Japan
*Corresponding author: Yoshinari Minami, Advanced Science-Technology Research Organization, Japan
Submission: November 19, 2018;Published: November 26, 2018
Volume1 Issue3 November 2018
As is well known in General Relativity, gravity is generated by a curved space. The curvature of space and the size of curved space region determine the gravitational acceleration. Curvature of space is formed in a concentric sphere state around the celestial body by the mass of celestial body like the Earth.
Minami derived the equation of curvature of space induced by magnetic field in 1988 [1]. It was found that this equation was accordance with the equation that Levi-Civita considered (i.e., the static magnetic field creates scalar curvature) by Minami in 1995 [2].
where is a magnetic field with Tesla and R00 is a major component of spatial curvature (1/m2 ).
The major component of curvature of space R00 can be produced by not only mass density but also magnetic field B (see APPENDIX A: Curvature Control by Magnetic Field). Above equation indicates that the major component of spatial curvature can be controlled by magnetic field.
The curvature of flat space R00 is zero (strictly speaking, only 20 independent components of Riemann curvature tensor Rpijk are zero), then the gravitational acceleration becomes zero. A curved space is generated not only by mass density but also by magnetic field or electric field. In case that the intensities of the magnetic field B and the electric field E are equal, the value of is about seventeen figures smaller than the value of . As a consequence, the electric field only negligibly contributes to the spatial curvature as compared with the magnetic field. Accordingly, it is effective that the space can be curved by magnetic field. Since the region of curved space produces the field of acceleration, the massive body existing in this acceleration field (i.e. curved space region), is moved in accordance with Newton’s second law.
Ultimately, it can be said that the magnetic field can be made equivalent to the gravitational field by the action of curving the space [3-6].
Let us consider the electromagnetic energy tensor Mij . In this case, the solution of metric tensor gij is found by
Eq (A.1) determines the structure of space due to the electromagnetic energy.
Here, if we multiply both sides of Eq (A.1) by gij , we obtain
The following equation is derived from Eqs.(A.2) and (A.3)
Substituting Eq.(A.4) into Eq.(A.1), we obtain
Using antisymmetric tensor ij f which denotes the magnitude of electromagnetic field, the electromagnetic energy tensor Mij is represented as follows;
Therefore, for M, we have
Accordingly, substitutingM = 0 into Eq.(A.5), we get
Although Ricci tensor Rij has 10 independent components, the major component is the case of i = j = 0 , i.e., R00 . Therefore, Eq.(A.8) becomes
On the other hand, 6 components of antisymmetric tensor fij = − fji are given by electric field E and magnetic field B from the relation to Maxwell’s field equations
Substituting Eq.(A.10) into Eq.(A.6), we get
Finally, from Eqs.(A.9) and (A.11), we obtain
where
B is a magnetic field in Tesla and R00 is a major component of spatial curvature(1/m2 ) .
© 2018 Yoshinari Minami. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and build upon your work non-commercially.