We develop a theoretical framework that allows us to compare electromagnetism and gravitation in a fully covariant way. This new scenario does not rely on any kind of approximation nor associate objects with different operational meaning as it's sometime done in the literature. We construct the electromagnetic analogue to the Riemann and Weyl tensors and develop the equations of motion for these objects. In particular, we are able to identify precisely how and in what conditions gravity can be mapped to electrodynamics. As a consequence, many of the gemometrical tools of General Relativity can be applied to Electromagnetism and vice-versa. We hope our results would shed new light in the nature of electromagnetic and gravitational theories.
We find the quantum power emitted and distribution in $3+1$-dimensions of relativistic acceleration radiation using a single perfectly reflecting mirror via Lorentz invariance demonstrating close analogies to point charge radiation in classical electrodynamics.
The effect of induced Riemann geometry in nonlinear electrodynamics is considered. The possibility for description of real gravitation by this effect is discussed.
We consider an approach to unification of the gravitational and electromagnetic interactions based on the existence of an effective Riemannian space in nonlinear electrodynamics. In the context of this approach, we discuss the possibility of screening the gravitational field.
We give a conceptual exposition of aspects of gravitational radiation, especially in relation to energy. Our motive for doing so is that the strong analogies with electromagnetic radiation seem not to be widely enough appreciated. In particular, we reply to some recent papers in the philosophy of physics literature that seem to deny that gravitational waves carry energy. Our argument is based on two points: (i) that for both electromagnetism and gravity, in the presence of material sources, radiation is an effective concept, unambiguously emerging only in certain regimes or solutions of the th…
The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics (EM) and magnetohydrodynamics (MHD) have benefited from a large number of evolution schemes that are able to enforce these constraints and are easily applicable to curvilinear coordinates, unstructured meshes, or N-body simulations, many of these techniques cannot be straightforwardly applied to existing formulations of the Einstein equations. We develop a 3+1 a formulation of the Einstein equations which shows a st…
Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution---the exact seven parameter solution of Plebański--Demiański (PD)---to demonstrate these analogies for a physically meaningful spacetime: The two quadratic curvature invariants $\bf{B}^2-\bf{E}^2$ and $\bf{E}\cdot\bf{B}$ are evaluated analytically. In the asymptotically flat case, the leading terms of $\bf{E}$ and $\bf{B}$ can be interpreted as gravitoelectric mass and gravitoelectric current of the PD solution, respectively, if there are no gravitomagnetic mono…
We derive the equations for the odd and even parity perturbations of coupled electromagnetic and gravitational fields of a black hole with an electric charge within the context of general nonlinear electrodynamics. The Lagrangian density is a generic function of the Lorentz invariant scalar quantities of the electromagnetic fields. We include the Hodge dual of the electromagnetic field tensor and the cosmological constant in our calculations. For each type of parity, we reduce the system of Einstein field equations coupled to nonlinear electrodynamics to two coupled Schrödinger-type wave equat…
This paper aims to investigate the astrophysical applicability of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov (Ann. Phys. Berlin 2017, 529, 170073). Theoretical calculations of the bending angles and gravitational redshifts from the theory of general relativity are studied numerically by using the stellar data of charged compact objects and a hypothetical quark star model. Calculations have revealed that although the theoretical outcomes differ from the linear Maxwell case, the plotted bending angles coinci…
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…
We consider the most general torsional completion of gravitation together with electrodynamics for the Dirac spinorial material fields, and we show that consistency arguments constrain torsion to be completely antisymmetric and the dynamics to be parity-invariant and described by actions that are either least-order derivative or renormalizable.
Effective Riemann space effect of vacuum nonlinear electrodynamics is considered in the context of theory for unified gravitation and electromagnetism. The electromagnetic four-vector potential in the scope of Born-Infeld nonlinear electrodynamics model is considered as the unified field. The electromagnetic interaction appears naturally in the first perturbation order by the small field of distant material objects. The gravitational interaction appears naturally in the appropriate second order. In this case the effective metric components contain the corresponding energy-momentum tensor compo…
We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called "1+3 formalism", and the analogy based on tidal tensors. Both are reformulated, extended and generalized. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. New results within …
The most general classical electrodynamics which still respect the linear superposition principle but allow for otherwise arbitrary birefringence require, and imply, a refined spacetime geometry described by a fourth-rank tensor field. Canonical gravitational dynamics for this geometry, if required to co-evolve in causally consistent fashion with the electromagnetic field, were shown to be constructively determined by gravitational closure of the birefringent electromagnetic field equations. For weak gravitational fields of the resulting birefringent refinement of classical Einstein-Maxwell th…
We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the fol…
We consider the unification problem for the gravitational and electromagnetic interactions and its possible solution on the basis of the existence of an effective Riemannian space in nonlinear electrodynamics
Explicit Robinson--Trautman solutions with electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones. In all cases the electromagnetic field singularity is removed while the gravitational one persists. The models resolving curvature singularity were not possible to generalize to Robinson--Trautman geometry indicating that the removal of singularity in associated spherically symmetric case is just a consequence of high symmetry. We show that the solutions are generally of algebraic type II but reduce to t…
In the present paper a geometrization of electrodynamics is proposed which makes use of a generalization of Riemannian geometry considered already by Einstein and Cartan in the 20ies. Cartan's differential forms description of a teleparallel space-time with torsion is modified by introducing distortion 1-forms which correspond to the distortion tensor in dislocation theory. Under the condition of teleparallelism, the antisymmetrized part of the distorsion 1-form approximates the electromagnetic field, whereas the antisymmetrized part of torsion contributes to the electromagnetic current. Carta…
This research aims to develop a new approach toward a consistent coupling of electromagnetic and gravitational fields by using an electron that couples with a weak gravitational potential by means of its electromagnetic field. We find the value of the tiny coupling constant of gravity with electromagnetic fields, which depends on the speed of light and a universal minimum speed that represents the lowest limit of speed for any particle. Such a minimum speed, unattainable by particles, represents a preferred reference frame associated with a background field that breaks the Lorentz symmetry. Th…
We study the linear post-Newtonian approximation to general relativity known as gravitoelectromagnetism (GEM); in particular, we examine the similarities and differences between GEM and electrodynamics. Notwithstanding some significant differences between them, we find that a special nonstationary metric in GEM can be employed to show {\it explicitly} that it is possible to introduce gravitational induction within GEM in close analogy with Faraday's law of induction and Lenz's law in electrodynamics. Some of the physical implications of gravitational induction are briefly discussed.
Coupled Gravitoelectromagnetic Response of a Magnetically Supported Generalized Hayward Black Hole in Nonlinear Electrodynamics
Centre for Cosmology, Astrophysics and Space Science (CCASS), GLA University（宇宙学、天体物理学和空间科学中心（CCASS），GLA大学）；Department of Physics, Mari.C., Islamic Azad University（伊斯兰阿扎德大学物理系，马里克）；Department of General Studies (Mathematics), Jubail Industrial College（朱拜勒工业学院普通研究部（数学））；PTC Software Inc. India（印度PTC软件公司）
The illuminating role of differential forms in electromagnetism is seldom discussed in the classroom. It is the aim of this article to bring forth some of the relevant insights that can be learnt from a differential forms approach to E\&M. The article is self-contained in that no previous knowledge of forms is needed to follow it through. The effective polarization of the classical vacuum due to a uniform gravitational field and of the quantum vacuum in the Casimir effect are used to illustrate the power and easiness of interpretation of differential forms in dealing with electromagnetism in n…
Given the recent direct measurement of gravitational waves (GWs) by the LIGO-VIRGO collab- oration, the coupling between electromagnetic fields and gravity have a special relevance since it opens new perspectives for future GW detectors and also potentially provides information on the physics of highly energetic GW sources. We explore such couplings using the field equations of electrodynamics on (pseudo) Riemann manifolds and apply it to the background of a GW, seen as a linear perturbation of Minkowski geometry. Electric and magnetic oscillations are induced that propagate as electromagnetic…
We study quasinormal modes related to gravitational and electromagnetic perturbations of spherically symmetric charged black holes in nonlinear electrodynamics. Beyond the linear Maxwell electrodynamics, we consider a class of Lagrangian with higher-order corrections written by the electromagnetic field strength and its Hodge dual with arbitrary coefficients, and we parametrize the corrections for quasinormal frequencies in terms of the coefficients. It is confirmed that the isospectrality of quasinormal modes under parity is generally violated due to nonlinear electrodynamics. As applications…
There is a set of first-order differential equations for the curvature tensor in general relativity (the curvature equations or CEs for short) that are strikingly similar to the Maxwell equations of electrodynamics. This paper considers whether Mother Nature may have used the same basic pattern for her laws of gravitation and electrodynamics, in which case the CEs might be viewed as the field equations of gravitation in place of Einstein's equation. This is not a new theory of gravitation (because the curvature equations are derivable from Einstein's equation), but rather is a mild reinterpret…
We propose a new approach to a physical analogy between General Relativity and Electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations. The following realisations of the analogy are given. The first one matches linearised gravitational tidal tensors to exact electromagnetic tidal tensors in Minkwoski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultra-stationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third we …
A model of nonlinear electrodynamics with the Lagrangian density ${\cal L} = -(1/β)\arcsin(βF_{μν}F^{μν}/4)$ is proposed. The scale invariance and the dual invariance of electromagnetic fields are broken in the model. In the limit $β\rightarrow 0$ one comes to Maxwell's electrodynamics and the scale and dual invariances are recovered. We investigate the effect of coupling electromagnetic fields with the gravitational field. The asymptotic black hole solution is found which is similar to the Reissner-Nordström solution. We obtain corrections to Coulomb's law and to the Reissner-Nordström soluti…
We establish a new model of coupling between a cosmic dark fluid and electrodynamic systems, based on an analogy with effects of electric and magnetic striction, piezo-electricity and piezo-magnetism, pyro-electricity and pyro-magnetism, which appear in classical electrodynamics of continuous media. Extended master equations for electromagnetic and gravitational fields are derived using Lagrange formalism. A cosmological application of the model is considered, and it is shown that a striction-type interaction between the dark energy (the main constituent of the dark fluid) and electrodynamic s…
Probing Bardeen-Kiselev black hole with cosmological constant caused by Einstein equations coupled with nonlinear electrodynamics using quasinormal modes and greybody bounds
We formulate axion-electrodynamics and magnetohydrodynamics (MHD) in the cosmological context assuming weak gravity. The two formulations are made for a general scalar field with general $f(ϕ)$-coupling, and an axion as a massive scalar field with $ϕ^2$-coupling, with the helical electromagnetic field. The $α$-dynamo term appears naturally from the helical coupling in the MHD formulation. In the presence of the electromagnetic coupling, however, the Schrödinger and hydrodynamic formulations of the coherently oscillating axion are {\it not} available for the conventional $ϕ$ coupling; instead, …
We present a first-principles' prediction that two charged particles of masses M_1 and M_2 separated R apart in a dielectric vacuum act on each other always an attractive force in addition to other known forces in between. This component attractive force on one charge results as the Lorentz force in the radiation depolarization- and magnetic- fields of the other charge, being an attractive radiation force, and is in addition to the ordinary repulsive radiation force. The exact solution for the attractive radiation force is F_g=G' M_1M_2/R^2, an identical formula to Newton's law of gravitation.…
