A Possible Reinterpretation of Einstein’s Equations

Bouda, A.; Belabbas, Abdelmoumene

doi:10.1007/s10773-010-0454-7

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…As suggested in [10], this will induce a dependence on the test particle properties of the electromagnetic field in the high energy domain. This intriguing feature was also discussed in the context of the links established between gravitation and electromagnetism [11].…”

Section: Introductionmentioning

confidence: 90%

On the Fock Transformation in Nonlinear Relativity

Bouda

Foughali

2012

Mod. Phys. Lett. A

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In this paper, we propose a new deformed Poisson brackets which leads to the Fock coordinate transformation by using an analogous procedure as in Deformed Special Relativity. We therefore derive the corresponding momentum transformation which is revealed to be different from previous results. Contrary to the earlier version of Fock's nonlinear relativity for which plane waves cannot be described, our resulting algebra keeps invariant for any coordinate and momentum transformations the four dimensional contraction pµx µ , allowing therefore to associate plane waves for free particles. As in Deformed Special Relativity, we also derive a canonical transformation with which the new coordinates and momentum satisfy the usual Poisson brackets and therefore transform like the usual Lorentz vectors. Finally, we establish the dispersion relation for Fock's nonlinear relativity.

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Section: Introductionmentioning

confidence: 90%

On the Fock Transformation in Nonlinear Relativity

Bouda

Foughali

2012

Mod. Phys. Lett. A

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“…Moreover, we should remember that Einstein's field equations actually contain terms which depend on the pressure and stresses as well and, if these terms were taken into account, then we would also get effects with no electromagnetic analogue − see, for instance, the Matte-Bel decomposition of Riemann tensor [69,70]. It should be mentioned further that attempts to remove the factor 4 in (31) were also considered [30][31][32][33][34][35]; these attempts however basically try to redefine the gravitomagnetic fields or potentials but, in general, the resulting gravitational Maxwell equations become different from that obtained in the electromagnetic theory (see also [71][72][73] for alternative perturbative methods that seems to successfully reproduce the Maxwell equations for gravity without the factor of 4 in the magnetic force above).…”

Section: A Thought Experimentsmentioning

confidence: 99%

Covariant theory of gravitation in the framework of special relativity

Vieira

Brentan

2018

Eur. Phys. J. Plus

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In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a magnetic-like force must be present whenever two or more bodies are in motion. The exact expression for this gravitomagnetic force is then derived purely from special relativity and the consequences of such a covariant theory are developed. For instance, we show that the gravitomagnetic fields satisfy a system of differential equations similar to the Maxwell equations of electrodynamics. This implies that the gravitational waves spread out with the speed of light in a flat spacetime, which is in agreement with the recent results concerning the gravitational waves detection. We also propose that the vector potential can be associated with the interaction momentum in the same way as the scalar potential is usually associated with the interaction energy. Other topics are also discussed, for example, the transformation laws for the fields, the energy and momentum stored in the gravitomagnetic fields, the invariance of the gravitational mass and so on. We remark that is not our intention here to propose an alternative theory of gravitation but, rather, only a first approximation for the gravitational phenomena, so that it can be applied whenever the gravitational force can be regarded as an ordinary effective force field and special relativity can be used with safety. To make this point clear we present briefly a comparison between our approach and that based on the (linearized) Einstein's theory. Finally, we remark that although we have assumed nothing from the electromagnetic theory, we found that gravity and electricity share many properties in common -these similarities, in fact, are just a requirement of special relativity that must apply to any physically acceptable force field.

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“…We therefore conclude that the time-dependence of the vector GEM potential A is directly related to the spatial components of the metric perturbationsh ij . If these components are altogether ignored in the analysis, as in the traditional GEM ansatz [15], the time-dependence of A is automatically eliminated (on this, see also [18]).…”

Section: Novel Ansatzes For the Metric Perturbationsmentioning

confidence: 99%

“…A different perspective, that has attracted considerable attention over the years, is the one adopted in the theory of Gravito-electromagnetism (GEM) [10] [11] [12] [13] [14][15] [16] [17] [18] [19]. In this, the dynamics of the gravitational field is described in terms of quantities met in electromagnetism.…”

Section: Introductionmentioning

confidence: 99%

Novel ansatzes and scalar quantities in gravito-electromagnetism

Bakopoulos

Kanti

2017

Gen Relativ Gravit

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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.

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A Possible Reinterpretation of Einstein’s Equations

Cited by 5 publications

References 10 publications

On the Fock Transformation in Nonlinear Relativity

On the Fock Transformation in Nonlinear Relativity

Covariant theory of gravitation in the framework of special relativity

Novel ansatzes and scalar quantities in gravito-electromagnetism

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