From GEM to Electromagnetism

arXiv:1610.08357 [gr-qc]

This work is focused on the theory of Gravitoelectromagnetism (GEM). In the first part of this work we present a brief review of gravitoelectromagnetism, we locate and discuss all the problems which appear in this approach. We also try to avoid these problems by proposing new approaches in which we use the additional degrees of freedom of the gravitational field. In the second part of this work, we review our previous work regarding the construction of a tensorial theory, using the formalism of General Relativity, which aims to describe the true electromagnetism. We also extend this theory in order to make it more realistic. Finally in the third part of this work, we investigate the existence of gravitational invariants similar to the electromagnetic ones.

Gen.Rel.Grav. 49 (2017) no.3, 44

In this work, we focus on the theory of gravito-electromagnetism (GEM)—the theory that describes the dynamics of the gravitational field in terms of quantities met in electromagnetism—and we propose two novel forms of metric perturbations. The first one is a generalisation of the traditional GEM ansatz, and succeeds in reproducing the whole set of Maxwell’s equations even for a dynamical vector potential A . The second form, the so-called alternative ansatz, goes beyond that leading to an expression for the Lorentz force that matches the one of electromagnetism and is free of additional terms even for a dynamical scalar potential Φ . In the context of the linearised theory, we then search for scalar invariant quantities in analogy to electromagnetism. We define three novel, 3rd-rank gravitational tensors, and demonstrate that the last two can be employed to construct scalar quantities that succeed in giving results very similar to those found in electromagnetism. Finally, the gauge invariance of the linearised gravitational theory is studied, and shown to lead to the gauge invariance of the GEM fields E and B for a general configuration of the arbitrary vector involved in the coordinate transformations.

2010

Classical gravitation is so similar to the electrostatic that the possible unification has been investigated for many years. Although electromagnetism is formulated now successfully by quantum field theory, this paper proposes a simple approach to describe the electromagnetism from the macroscopic perspective of general relativity. The hypothesis is based on two charged particles that cause disturbance energy sufficient to disrupt the space-time and explain approximately Maxwell's equations. Therefore, with such this simple idea, we suggest the possibility that the geometric relationship between electromagnetism and gravitation is not yet fully exhausted.

arXiv: General Relativity and Quantum Cosmology, 2005

The formalism of electric - magnetic duality, first pioneered by Reinich and Wheeler, extends General Relativity to encompass non-Abelian fields. Several energy Tensors T^uv with non-vanishing trace matter are developed solely as a function of the field strength tensor F^uv, including the Euler tensor, and tensors for matter in flux, pressure in flux, and stationary pressure. The spacetime metric g_uv is not only a solution to the second-order Einstein equation based on T^uv, but is also constrained by a third-order equation involving the Bianchi identity together with the gravitational energy components kappa_u for each T^uv. The common appearance of F^uv in all of the T^uv and kappa_v makes it possible to obtain quantum solutions for the spacetime metric, thereby geometrizing quantum physics as a non-linear theory.

International Journal of Modern Physics D, 2001

The integral formulation of Maxwell's equations expressed in terms of an arbitrary observer family in a curved spacetime is developed and used to clarify the meaning of the lines of force associated with observer-dependent electric and magnetic fields.

Classical and Quantum Gravity, 1998

We develop and apply a fully covariant 1 + 3 electromagnetic analogy for gravity. The free gravitational field is covariantly characterized by the Weyl gravito-electric and gravito-magnetic spatial tensor fields, whose dynamical equations are the Bianchi identities. Using a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, we exhibit the covariant analogy between the tensor Bianchi equations and the vector Maxwell equations. We identify gravitational source terms, couplings and potentials with and without electromagnetic analogues. The nonlinear vacuum Bianchi equations are shown to be invariant under covariant spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields. We construct the super-energy density and super-Poynting vector of the gravitational field as natural U (1) group invariants, and derive their super-energy conservation equation. A covariant approach to gravito-electric/magnetic monopoles is also presented.

1991

The numerous ways of introducing spatial gravitational forces are fit together in a single framework enabling their interrelationships to be clarified. This framework is then used to treat the “acceleration equals force” equation and gyroscope precession, both of which are then discussed in the post-Newtonian approximation, followed by a brief examination of the Einstein equations themselves in that approximation. 1

Annals of Physics, 1992

The numerous ways of introducing spatial gravitational forces are fit together in a single framework enabling their interrelationships to be clarified. This framework is then used to treat the "acceleration equals force" equation and gyroscope precession, both of which are then discussed in the post-Newtonian approximation, followed by a brief examination of the Einstein equations themselves in that approximation.

2006

The need to know the force exerted by moving body on ground of intriguing interplay between geometry and dynamics gives a possible introducing of gravitomagnetic (GM) field as an analogous to the magnetic field. The existence of such a field has straightforwardly been presented in two approaches based on special relativity (SR) only and SR plus gravitational time dilation (semi SR) for different cases. We treat these two approaches for when the cases are switched, using appropriate key points. Hence, we demonstrate that the strength of GM field in semi SR approach is twice SR approach. Then, we also discuss that the full linearized general relativity should give the same strength for GM field as semi SR, and hence, through an exact analogy with the electrodynamic equations, we present an argument for the best potential definition amongst those used in this issue. PACS number: 03.30. + p; 04.20. − q

2011