Abstract
In previous publications, we showed that Maxwell’s equations are an approximation to those of General Relativity when V<<c, where V is the velocity of the particle submitted to the electromagnetic field. This was demonstrated by showing that the Lienard-Wiechert potential four-vector A_u created by an electric charge is the equivalent of the gravitational four-vector G_u created by a massive neutral point when V<<c. In the present paper, we generalize these results for V non-restricted to be small. To this purpose, we show first that the exact Lagrange-Einstein function of an electric charge q submitted to the field due an immobile charge q_0 is of the same form as that of a particle of mass m submitted to the field created by an immobile particle of mass m_0. Maxwell’s electrostatics is then generalized as a case of the Einstein’s general relativity. In particular, it appears that an immobile q_0 creates also an electromagnetic horizon that behaves like a Schwarzschild horizon. Then, there exist ether gravitational waves constituted by gravitons in the same way as the electromagnetic waves are constituted by photons. Now, since A_u and G_u, are equivalent, and as we show, G_u produces the approximation, for V<<c, of g_u4 created by m_0 mobile, where the g_uv are the components of Einstein’s fundamental tensor, it follows that A_u+u_u produces the approximation, for V<<c, of Bet_u4 , where the Bet_uv created by m_0 and by q_0, generalize the g_uv.
Highlights
That is to say that we show that the exact Lagrange-Einstein function of an electric charge submitted to the field due an immobile charge and its motion equation are the same as those of a particle of mass submitted to only the field created by an immobile particle of mass
Conclusion regarding classical gravitation: Since, when =, and = 0, Eq (57) becomes Eq (14) which is an approximation of Eq (3), it follows that (57) can produce only an approximation of the exact motion equation of the (, ) submitted to the field created by the mass of velocity
⁄ will becomes ⁄2; this tensor ב is a solution of Einstein’s general relativity equations. It appears that Maxwell’s electromagnetism can be generalized as to be a case of the General Relativity, that is, the exact Lagrange-Einstein function of an electric charge submitted to the field due an immobile charge and its motion equation are the same as those of a particle of mass submitted to only the field created by an immobile particle of mass
Summary
In Zareski (2014) and in Sec. IX of Zareski (2015), we showed, in particular, that from the elastic ether theory it appears that the form of Maxwell’s Electromagnetism emerges as an approximation of General Relativity. IX of Zareski (2015), we have shown this fact in the case where the velocity of the particle is such that ≪ , that is to say that we have shown that Maxwell’s electromagnetism is of the same form as Newton’s gravitation We generalized Maxwell’s electrostatic to a case of Einstein’s general relativity It appears that an immobile creates an electromagnetic horizon that behaves like a Schwarzschild horizon, that is, when another electric charge q is attracted by and reaches this electromagnetic horizon, its velocity is there null. We arrive to the conclusion that, since in the approximation ≪ , and differs by only a constant multiplicative coefficient and since as we show, produces the approximation of , where one recalls that the are the components of Einstein’s fundamental tensor created by whether it moves or not, it follows that + produces the approximation for ≪ of ב , where the ב are the components of a tensor that generalizes Einstein’s fundamental tensor by taking into account the contribution of the electrical charge
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